From detailed reading of the book, plus the short story "The Day Before the Revolution," it is pretty clear that Odo's movement intended to take over all of the planet Urras and their relegation to the moon Anarres was a compromise. Apparently there were enough Odonians and people likely to switch over to the Odonian side that the rulers of the dominant Urrasti nations judged they could not push forward for complete extermination without making more revolutionaries through martyrdom than they'd eliminate, and since offering them a whole habitable moon was an option, they did so to bring the deterioration of their position to a speedy end.
Note that one nation, Thu, did succumb to an Odo-influenced movement, but without us getting a lot of details it seems it went Stalinist somehow. We might regard that as some sort of unhappy accident, and that it would have been possible for Thu to remain truer to Odo's vision, which would have meant a knock-down, all out war with A-Io while that nation's working classes quickly went Odonian, the army presumably mutinies and surrenders to the Thuvians, and with both leading powers gone Odonian the rest of the hemisphere would fall like dominoes and then the other hemisphere (known only for having the "backward" nation Benbili located there) presumably gets enlightened in an inexorable process. Then Anarres would presumably become a minor scientific and mining outpost.
Since Thu went centralist (and we might more reasonably assume that since the Odonians don't win in A-Io yet remain popular there among the working classes, that the upper classes have very effective ways of counterattacking that account for the corruption of the Thuvian revolution) a key part of the exile settlement was that the "archist propertarians" controlled the spacecraft shuttling between the worlds, were bought off with promises to provide certain key minerals that had become rare on Urras, and between this small economic incentive and the much more preoccupying concern that Odoism be kept quiet and invisible back on Urras, and that martyrdom would promote their cause, the incentive of the capitalists who own the space ships is to keep the contact ongoing but very limited, tightly under their control. And that the Anarresti are thus safe and free to do whatever they want.
You call Anarres "very" habitable, and it certainly is compared to say Luna or Mars, in that it has a breathable atmosphere and some relatively small seas. Compared to Earth, or Urras, though, it is pretty bleak, with just one genus of multicellular plant that takes grassy or somewhat tree-like forms and no animals ever mentioned, not even any kind of bugs. (The Odonians I think did import some plants, very carefully cultivated in greenhouses at Abbenay and maybe a few other scattered places, either being very careful not to let them run wild or finding that they never do, because the environment outside greenhouses is too harsh for useful plants to establish themselves). They eat grain made from some native "holum" species and there are some kinds of fish in the seas.
Now if we had a Terran close analog to Odo, and her movement was as effective as in the book, presumably threatening to take over 19th century France and Britain and the other industrializing powers of Europe, yet failing to consolidate their victory anywhere on terms acceptable to true Odonians, and the surviving governmental/propertied classes of these European powers were similarly deterred from trying to simply massacre the lot of them (as in Wellington's time, the Chartist movement, 1848, or the massacre of the Paris Commune, so it is definitely a "normal" option to try to use simple terror to subdue and subjugate such rebels) and instead offer them a colony somewhere on Earth, it would be a different situation in that the "archists" would be compelled to find someplace where the borders could be efficiently watched so the subversives don't get out to spread their dangerous appeal to revolution. Giving them all of Australia for instance would seem broadly parallel, but could even the RN hope to patrol the seas surrounding, watching the shores for any wildcat boats bold "Australisti" might launch in the hope of finding brotherhood in say the Dutch East Indies, or Indochina, India or China itself? Let alone the danger that having slipped the blockade, they might land somewhere along the way to Europe or America hoping to spread another generation of revolutionary action in the strongholds of capitalism itself?
Odo is not Marx or Lenin, though she has analogies to both of them, mostly to Marx. Her detailed analysis is not available to us of course--one can infer a lot from the novel, and if as I write and later as others read God Willing LeGuin herself is still alive we might want to pick her brains for more insights. But Odo clearly differs from Marx, and even Lenin, in her attempt to chart out in positive and detailed ways how revolutionary people should live, in mundane activity as well as high-flown revolutionary action. This is exactly what Karl Marx prided himself on not doing, on spinning Utopias in the mind and then simply trying to impose them in real life directly. It is what the other revolutionaries of his day and afterward routinely did, and Marx scorned them for it, claiming that it was necessary to comprehend the dialectical course historical materialism was bound to follow given existing conditions, and using that knowledge smooth the way most efficiently for the inevitable emergence of mature humanity in full control of the powers given it by science and intelligently organized collective action. The details of this were supposed to be established largely by capitalist development followed by what Marx, and Lenin, assumed would be common-sense implementation of technocratic wisdom geared toward the collective good. It wasn't his responsibility and would be a dangerous distraction to try to predict that course in detail, he figured. Odo on the other hand dived into that task as her primary goal, her book The Social Organism being in one her Manifesto and her Capital, scorning to analyze, save in passing, the internal mechanisms of capitalism in favor of outlining the workings of a functional society of free people.
In terms of internal evidence in the book, she did a good job of it too, hitting upon a sustainable and robust model that the Anarresti live under and from the internal workings as shown in the chapters set on that planet, have little reason to complain of. (To be sure I've met people who have read the book, or claimed to have, who dismiss Annares as "evil," though they declined to get into a conversation as to why). Certainly the book itself exemplifies as well LeGuin's subtitle, "An Ambiguous Utopia," by showing forces at work that undermine Odo's essential vision, demonstrating why Odonians must live a "permanent revolution," each generation challenging these pernicious tendencies. But they have the social resources to do so should they so will, and presumably someone always does--in his generation, it is Shevek and his friends who lead such a movement.
The book blew my mind when I read it in junior high as it became clear to me pretty near the beginning that I was reading about a successful and admirable communist society; my background as a child of a conservative military and Roman Catholic family hardly allowed me to be complacent about it, and I had to assume that there were sad tendencies of some kind or other that prevented such a society from existing. Then in college I stumbled upon accounts of the Summerfield school in Britain that also purported to work upon principles of no coercion and had to wonder just how strong these barriers really were, and whether their nature was as deep-rooted as I had been largely led to believe.
But the question of just how sustainable such a society would be remains open of course, and in real life we have to expect that powerful forces seeking to undermine and if possible destroy it would continue to be brought against it. In the scenario of the two worlds, the cultural embargo enforced by the Urrasti (apparently tantamount to the rulers of A-Io, though presumably the Thuvian rulers also cooperate at least tacitly by not choosing to attempt to challenge it, in their own selfish interests although they'd clearly have the technical ability to do so with rockets to Anarres of their own--but aside from the risk of subversive blow-back in Thu itself, they also know the Odonians on the moon will scorn them for their betrayal and perversion of Odo's teachings and frankly prefer to deal with open pirates like the A-Io gang) also works for the Anarresti, preventing would-be subversives and sleeper agents from being planted among them. (To be sure, I'd think that on the whole, any such agent, no matter how devoted initially to the A-Io way, or Thuvian, would be persuaded to change their allegiance after a few months on Anarres, even in their worst times such as the drought known as the Dust in the book).
To be more realistic than LeGuin, I suspect that the idea of simply nuking the hell out of Anarres would never be too far from the minds of many A-Io security types. With the low levels of communication, with wildcat radio being almost completely unknown and with the ability of the governments involved to control spacecraft and powerful telescopes, an overwhelming nuclear strike on the major settlements, accompanied by seeding the planet with fallout with dirty bombs and perhaps targeted biowarfare germs, would immediately silence the survivors (especially if a space force remained in orbit for some time to observe any sign of life and drop reserve bombs on anyone who shows them) and assure the eventual death of the colony. It might even be possible to claim, to the masses on Urras, that some natural fluctuation in Anarres's environment (all too plausible in view of its marginality, with that single genus of plants suggesting a recent near-extinction event) or a meteor strike was responsible. It might not be entirely believed but might be doable with the regime having some confidence of covering its tracks, and persuading foreign rivals to keep quiet in return for considerations including the quiet observation that they too do benefit from the removal of the ideological "threat of a good example" as Noam Chomsky put it here on Earth. Or someday someone might want to just admit to this genocide and cite it as a good reason why extremists should not hope for a safe refuge and face "reality."
If we imagine it happening on Earth in the 19th century, this option is not available (until the 1950s anyway). But neither is there anyplace where the anarchists can be safely deported and deemed contained.
Perhaps then a more realistic path to such a result is a revolution in place, intending to become global, that is contained. Let us say a vast rising in say France results in a dissected checkerboard of strongholds of both revolution and reaction, and the revolution extends into Spain as well. But the propertarian powers rally, defining a cordon of non-communication and propaganda on France's northern and eastern borders, finding or manufacturing enough horror stories and disgruntled locals to keep up counterrevolutionary morale in a Grand Alliance composed of say mostly Germans with a lot of Belgians, Dutch, emigre French and Spaniards/Portuguese, and leadership, financing and naval supremacy contributed by Britain, perhaps with some US aid going into the pot too. Both sides are riddled with subversion of course, but the Grand Coalition through harsh police and terror tactics manages to capture and kill, or drive into exile (to the French lines or by sea, behind them into refuge) the leading subversives on their side and lots of followers too, the rest being cowed. Meanwhile in France, large numbers of die-hard counterrevolutionaries also are being gradually purged and forced into concentrated pockets--they weaken the "Odonian" front enough that the desperate and well-funded Coalition forces them south, past Paris and other northern cities they lose, and on south into Provence and Aquitaine. But without the menacing front lines, despite Spanish general conservatism, the revolution in Spain gets stronger, expelling large numbers of irreconcilables by sea where the RN picks them up and escorts them to be settled as refugees and recruited to the reactionary forces. Gradually the French Odonians also filter south into Spain, to be settled as refugees there and to form new Odonian communities (assuming here too an artificial language, analogous to Pravic, smooths the way of dissolving nationalist chauvinism on both sides of the cultural divide, so a new Odonian society is forming in Iberia). The day comes when the revolutionaries and reactionaries come to terms, as the Odonian resistance is getting firmer as they figure out how to supply themselves with available resources and become more effective fighters forged on the field of battle, while the rebels also recognize they are hemmed in and cannot expect a mass rising in Europe around them to relieve them. Both sides find it prudent and necessary to talk truce. The Coalition cannot allow the rebels such ports as Bordeaux or Marseilles and in effect the border settled on is the ridgeline of the Pyrenees. Spain and Portugal are deemed lost and fully evacuated of anti-revolutionaries--perhaps the British still hold Gibraltar but there is no communication across that line. Except for one tightly watched border fort on the Mediterranean coast, to which either side can bring goods by coastwise ship or over land as they choose, and at which communications are as tense and guarded as those between North and South Korea OTL, there is no communications or trade across the no-mans-land of the mountain ridge--it is legally granted to the revolutionaries but not one meter downslope, and watching posts on the north side of the border guard against any such intrusions. By sea, RN and other coalition forces patrol from French and British ports, the Atlantic, Mediterranean islands and the Moroccan coast to guarantee no Odonian ships set out from Iberia.
Thus we get Spain/Portugal as Anarres, not totally inappropriate considering the anarchist role in the OTL Spanish Civil War period. Huge numbers of conservative Spanish have either been killed or fled, largely settling in France which is depopulated by war and by "desertion" of huge sections of its urban and somewhat smaller sections of its rural working classes southward.
I could sketch out some other scenarios too. OTL many Utopians made for the USA, where they found native-born US citizens willing to join them in their various settlement schemes. If we picture an alt-Odo crafting a parallel version of The Social Organism that appeals broadly, many colonies that OTL were separate, founded on more or less divergent principles as well as setting themselves off from the mainstream US population, might reform along parallel lines, be more successful internally, and federate with each other, becoming a strong and disturbing element in larger US society. Surely they would seek for a while an era of good feeling, stressing their commonalities with larger US ideals, but I suppose eventually a break must come sometime, somewhere. Say colonies in New England find they have provoked a strong regional party dedicated to subduing them or throwing them out, and are driven out west to swell other colonies--that already have been provoking enemies there even while recruiting new friends who join them, leading to yet more showdowns and drawing in the Federal Government, increasingly influenced by the anti-communal party. (Southern slaveholders would be threatened by their mere existence, even if the group of Utopians adopts a prudent silence on the slavery question--but to keep such a silence would be very untrue to 19th century revolutionary ideals, so as their bridges burn and the nation polarizes around the revolutionary question, the anarchists would more and more take an abolitionist position. If things come to a head well before 1860, the result might be an exodus comparable to the Mormon push west of OTL. The anarchists might preempt Mormonism completely, or make Smith's followers look respectable by comparison and thus leave the Latter Day Saints a relatively secure place in the Midwest, especially once the Utopians evacuate, so the territory we think of as "Deseret" in the pre-Civil War period might become instead Annares.
As you have noted, there is no habitable place on Earth where a bunch of Utopians can settle without first extirpating or assimilating some Native people or other. In the Iberian case it is a process of sociological cleansing in the course of a bitter revolutionary civil war. Here in America it could instead be a matter of some hundreds of thousands of European-background revolutionaries with a humane pan-humanistic ideology shrewdly applying the seriously developed organizational principles of Odonianism to negotiate treaties with various Native American groups. It may be that these fail in many cases and the result is an Odonian-Allied Indian coalition defeating these, or driving them to US, Texan, British ruled northern, or Mexican territories to make their alliances with those powers. Assuming that the Odonians know what they are doing, they develop a hard core in the Great Basin which they flesh out to guarded mountain borders on the Rockies and in the west, on the coastal ranges. Presumably the established powers deny them plum territories like the California central valley, the Willamette-Columbia basin, or Puget Sound, and perhaps the USA manages to preserve a land connection Oregon. But in addition to Indian alliances, they also are subversive and might draw manpower from all the surrounding powers, making it risky for any of them to prosecute war against them lest their own armies be subverted and defect. It should not be too difficult for all these powers to preserve elite forces more or less immune to such subversion but it limits their ability to mobilize a mass crusade against them either.
If Odonianism is really scientific and an effective model for organization, it should be possible for them to preserve and expand scientific/technical abilities, starting at rudimentary levels with being able to become self-sufficient in gunpowder (assuming they first become self sufficient in food, which can be done in the Great Basin notably at Salt Lake, but also other little oases that with scientific sustainable techniques can manage to subsist a Spartan existence with some surplus left over to trade with the more weakly assimilated Indians, and perhaps other bands of desperadoes fleeing the authorities of the surrounding powers. Thus a core of intensely developed society at Salt Lake with colonies in places like the Lake Tahoe/Washoe region, etc, can be surrounded with scattered but materially enhanced autonomous Indians and various outlaw gangs that have come to terms. Basically they seek to replace the Wild West with an Anarchist West.
I gather that some Latter-Day Saints OTL developed an artificial language with new alphabet; if we parallel these Odonians, they have something like Pravic. Since they aren't setting a new planet all by themselves and are in demographic flux due to gaining new convert-recruits (while perhaps losing some people defecting back to the surrounding powers) it might become more of a regional universal second language than the mother tongue of a majority.
Here, there is no peaceful truce agreeing to a settled boundary; their borders fluctuate with the changing resolve of the conservative powers around them to challenge them versus the risk of subversion handing over provinces to them. Perhaps after a generation or two, warfare tends to end as the boundaries are fixed, but unlike an Australian or Iberian analogy the borders are hard to control. Conservative powers gradually learn it is hard to subvert the Odonians even with dedicated agents, who as likely as not might turn coat and return to subvert their home lands instead; Odonian inspired revolts in various countries more often than not come to grief, especially out of physical contact with help from Great Basin Anarres, causing a handful of refugees to filter thence and enrich the anarchist bastion's culture, and so the dream of revolution is checked elsewhere for the most part--but never quite exterminated either!
I'd want to game out US, Mexican and Canadian history very carefully in this scenario. Would the War with Mexico be butterflied away? If it starts at all in support of Texas, it would surely also develop an anti-Anarres component as well, but this by scenario largely comes to grief in the Western desert terrain the anarchists have adapted to--and made Native alliances in. Navaho and Pueblo peoples and Apaches with a reliable gun supply and coordinated generalship might be quite formidable for the US Army to deal with, particularly with soldiers deserting. They deserted OTL in Mexico, why not in the Rocky Mountain/Great Basin front, especially if offered refuges where people speak their languages and share a subversive version of their culture? In turn the sapping of US and Texan forces diverted northward might enable the Mexicans to do better, particularly if Odonian advisors offer alliance in return for rectification of the northern borders, asking Mexico to divest itself of largely worthless to them terrain in return not only for help in their current war but ongoing trade with value now coming to them from territory they gained nothing from when nominally holding it? I'd think Texas would wind up a US state, but with only part of New Mexico and Colorado. Similarly there would not be time for the Odonians to secure California and they might concede it on paper to Mexico, but the seaborne arm of the OTL campaign there ought to arrive, and some other path than OTL to the annexation of California to the USA would probably happen. But their claim inland of the Sierras would be very dubious! No good overland route would exist unless the Odonians conceded one. California might in effect become an island--indeed if the Odonians do well in making Native alliances northward, the whole West Coast might be cut off from USA east of the Rockies, with Anarresti influence reaching even up to British claims of OTL and annoying them too.
As for the Civil War--perhaps Abolitionist interests are weakened, as the radicals to the west suck the oxygen out of progressivism in the east, or reactionary dominance there turns the USA into an authoritarian/propertarian direction in which either Lincoln would never say the claims of Labor must precede those of Capital, or if he says it it brands him as a dangerous subversive who eventually moves west. If we assume that despite the cultural polarization, the coalition against Southern property owner dominance in the US government builds anyway, and abolitionists though weaker ally with Free Soilers and northern industrialists and so on, perhaps this opens the door for a detente, under an alt-Republican administration anyway, with the anarchists. If the South secedes, Washington might find common grounds enough with "Abbenay" on the Salt Lake and the Odonians and their autonomous cooperative allies might allow projects like a transcontinental railroad (that they run in the free sectors) and managed trade, in effect returning the OTL resources of the Great Basin to US industrialist hands. Anarresti volunteers of various stripes might even agree to assist the Union armies against the rebels--they surely will see through Southern claims against Union tyranny to the pro-slavery attitudes they deplore.
However such detente is also likely to lead to labor unrest in the USA, even if it first wins the Civil War. I suspect a more likely trajectory, from War with Mexico and Anarres days (probably known as the Western War in the USA) is that frustrated, not having gained California or the Southwest beyond Texas in general, finding the Anarres/Indian border tough to penetrate with the Pacific Coast of the continent being partitioned between Mexico and Britain, the USA becomes authoritarian, reaches a ready accommodation with southern slavery, and socially polarized between a revolutionary working class they are always purging with terror and some migration (by refugees, or sometimes exiles, to the west) and very propertarian reactionary society. One that does effectively develop a very powerful industrial system to be sure, with African-American slavery moving north to handle some strata of industrial labor (deemed appropriate for slaves) and a "white" workforce sociologically compensated for constrained opportunities (more social mobility upward by getting rich or providing diligent service to employers than in Europe, but obviously limited to a few and demanding very tight ideological conformity for these middle classes aspiring to be rich) by their white status above all colored people. Industrialism on such a basis is quite possible I suspect, though it would be less flexible than in a more apparently free society, and troubled by persistent underground subversion inspired by the western bastion. On the coast, the Anarresti would be forced to come to terms with British and Mexican authorities for access to the sea, not in their hands, with the deep-pocketed British Empire providing for heavy policing to offset the subversive influence--still losing people who defect and head inland to the land of freedom to be sure. After the Gold Rush (I suspect under nominal Mexican rule, but only because the British informally support it for concessions in California) California might be in constant danger of Odonian revolution; indeed all of Mexico might go "red" or whatever color is associated with Odonianism ITTL--at which point, in the midst of a vast continental revolution, both USA and Britain might be drawn into a costly war in the name of property and "order" that costs them dearly in defections and loss of some territory while they prop up authoritarian puppet states to hold the rest. At this point Anarres reaches the Pacific Coast to some degree and either Britain ponies up for a heavy blockade, or the world is forced to endure subversive ships making port at random, around the Pacific, then Indian Oceans, and getting into the Atlantic by two routes.
Assuming American Anarres cannot be crushed out of existence by a strong US Army, possibly with the aid of British and Mexican forces, sooner or later either Odonian society reaches some kind of plateau whereby it finds a niche in which it is not ideologically threatening to world stability, or it gets stronger as its peoples, poor per capita and few in number due to the sparse resources of the Great Basin, but rich per capita in terms of technical ability due to their wide and deep education and willingness to work for scanty personal rewards, leverage better territories to their control and wider and larger populations. If they get control of territories such as the Columbia river system, California with access to the sea via San Francisco Bay, or Puget Sound, then when they welcome in revolutionary refugees from all over the world they can settle them in better, less Spartan style without needing to encroach on their Indian allied peoples (who probably will assimilate to the revolutionary culture in time anyway) and develop really massive industrial forces to aid subversion in very widespread places. If they are strong enough to defy a crusade of all industrialized powers being brought against them they can break the defenses of the North American powers, and as the reactionaries exhaust themselves and build social tension in their own societies, revolutions inspired by them will break out behind the backs of their foes; if their power is stretched to the breaking point then the American Odonians can set up new fraternal bases overseas and from there, subvert their way outward to start the process of Odonian world revolution.
But as Napoleon said, "the one thing you can't do with bayonets is sit on them!" If the Odonians are to survive, and retain their revolutionary ideals, they have in their hands an ideological bayonet to counter the physical terrorizing ones of their archist foes, and thus they remain an existential threat to all of them no matter how peaceful they profess to be. If they live up to their ideals they will move to help "ammar" ("brothers", but non-gendered--siblings but with the emotion behind the word of either brother or sister--"comrades" in this case) struggling for their own freedom and thus all pretensions at peaceful innocence are gone, leaving only their sense of self-righteousness as being on the good side of history. On their side, the archists must always fear and suspect subversion; the permanent revolutionaries would plead guilty to the charge with a smile.
So for that reason, one would need contrived circumstances to have the Odonians living in their own little world, not acting to liberate the larger world and being left alone by it. As I game it out, it seems no matter which way they turn and where they might get a respite of some years or generations, either they struggle for ultimate world victory, or they are broken and destroyed (save as a subversive ideal that might indeed live on forever after their martyrdom). They can't get some grant of land on Earth and then just sit there forever.
So I guess I have to nay-say that aspect of your challenge. Can they survive? Quite possibly, if they can exist at all! Can it be side by side with a propertarian world? I'd say no. They need another planet, and even in that case as I said I think LeGuin was being pretty generous assuming they wouldn't all get massacred. The dynamics of class struggle might be drawn out across centuries to be sure, so that for those centuries both blocs exist side by side. But there would be no stability, not in the long run. They win, or they die.