The likelihood is difficult to ascertain. His actual plans were pretty solid and quite crafty. He had a very good understanding of several factors that worked in Christianity's favour, and made viable plans to alter those factors in
his favour. The major problem is that he also had a lot of other obsessions, and the chances of him getting killed to soon to see it through, being to pre-occupied during his life to see it through, or both being pre-occupied
and dying too soon are really quite considerable.
Then there's the other thing: the chances of him "re-establishing paganism" are actually exactly 0%... because whatever he may have claimed, that is
not what he was doing. He was creating a new religion, using the old traditions as the ritualistic and mythological basis, but (purposely!) copying the clerical structure of Christianity... and
deeply drenched in Neoplatonism. Had he succeeded, it would not have been in saving or restoring paganism, but in fundamentally altering it.
I've written some commentary on this matter in a previous thread, which I'll reproduce here in a tidied-up form:
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The weakness of various pagan religions compared to their monotheistic comparisons was a distinct lack of clear, all-encompassing doctrine and organisation. What Julian had in mind was actually along the lines of deliberately
stopping the fluid, syncretic character of the
Religio Romana. He was acutely aware of the harsh reality that when you get a competition between on the one hand a faith without a set orthodoxy or a universal clerical structure (and which is by definition tolerant of other deities), and on the other hand a religion with a defined orthodoxy and an organised clerical structure (which is also monotheistic and denies the very existence of all other gods)... the latter is going to win. Simply because the former tolerates the latter in its midst, while the latter will never tolerate the former. So if the former gains power, the latter can continue to bide its time... but when the latter gains enough power, the former gets killed off.
Julian's solution was, in all likelihood, the only realistic solution: it was to create an orthodoxy and a universal clerical structure for the
Religio Romana. Essentially, he wanted to define a definitive 'version' of the religion, and institute a priesthood to maintain that new orthodoxy. A canonical version of the ancient myths would be penned, in a document surely meant to explicitly rival the Christian scripture. He purposely tried to re-organise his own religion into something that was
structurally a lot more like Christianity. An all-ecompassing, organised priesthood. His own version of definitive religious texts. State sponsoring of his religion. Because he knew that a religion that has suvh organising capacity (as well as state backing) simply has a great advantage. Roman paganism was doomed to change, even if it won out over christianity due to Julian's efforts, because it would win out precisely by becoming far more like the Christian faith that Julian so despised. He was well aware of this irony, it seems, but his goal was to use the enemy's (obviously succesful) methods and instruments against them. A very good book that sets out Julian's character and his religous ideas and goals is Rowland B. E. Smith's
Julian's Gods: Religion and Philosophy in the Thought and Action of Julian the Apostate. Very briefly summarised (and omitting a
lot):
-- Julian planned to explicitly include a whole lot of Neoplatonism in the definitive texts of "the old religion", so he was very far from actually preserving, and more planning to change things in the direction
he liked. The Gods would, at least to some extent, be recast as 'representations' of the all-encompassing divine Absolute (or whatever name one might give to that). Elements from mystery religions would be deliberately syncretised and absorbed into the new religious 'canon'.
-- Julian was not planning to exterminate Christianity, or to fully end religious tolerance. (At least: he wouldn't ban Christianity until he had crucially weakened it and meanwhile consolidated his own religion. Smith argues that Julian obviously hated cChristianity a lot, and would probably have banned it for good at a later stage. Do note that this is Smith's reading of Julian's character, and based on conjecture.)
-- Certainly, heterodox (and localised) versions of the Roman-Hellenic religion would be tolerated. But the new orthodox version of the
Religio Romana would enjoy the favour of the state. Christianity would be tolerated, but hindered/discouraged. For instance, Christians would no longer be allowed to open schools (ensuring that education would fall to the religious schools of the
Religio Romana, which the state would fund).
-- Christian churches would no longer be tasked with the distribution of alms to the poor on behalf of the state. By Julian's time, Christian churches got state funding in quite a few instances, for the purpose of performing such charitable work. (Robin Lane Fox also goes into this, in
Pagans and Christians.) The whole problem was that in the old days, pagan temples had been funded by pious patricians, but this traditional conduct was in steep decline. Christianity kind of filled a developing vacuum, and its higher degree of organisation made it much better at 'temple charity' (or rather: church charity). So they kind of just... got that job. This obviously drew the poor to embrace Christianity. Julian knew that, and planned to make temple charity the task (and the exclusive
right) of his orthodox pagan priesthood and their temples, which would draw the poor to
his religion.
-- Finally, there would be a specific tax levied on all Christian churches, to repay the damage (real or perceived) that Christians had in the past inflicted on pagans, pagan temples etc.
Julian's reforms would entail that not only would Chistian churches be deprived of state funding while pagan temples would get that funding, but the pagan temples would also befit from gaining a similar organisation structure to Christianity. Christian churches, meanwhile, would thenceforth have to rely exclusively on donations by the faithful... while also getting taxed extra. I imagine there wouldn't be a lot left to spend on charity, while Julian's religion would be pretty flush with cash. All this would serve to encourage people to join Julian's religion, while make Christianity rather unattractive. The book I mentioned does a far better job laying out Julian's plans, as well as his ideas and beliefs. But what I've outlined above should really be enough to demonstrate that Julian wasn't stupid enough to ban Christianity outright, but that his plans were actually quite realistic and pragmatic. Barring unforseen circumstances, I'm actually pretty sure that a longer-lived Julian would probably have succeeded in defeating Christianity and making his own religion dominant-- provided he didn't get distracted by other matters, that is.
The thing is, the resulting religion would no longer have been the religion of Julian's ancestors. In saving what was left to save, he would have altered it on a fundamental level. It would be, ironically, a lot more 'Christian' in its character. Incidentally,
@Indicus pointed out (in the discussion where I first outlined all this) that there's another comparison available: the 'reborn' paganism of Julian would likely end up being a lot like Hinduism, as well. Certainly in the sense of "all deities being representations of a greater cosmic power", Julian's philosophical approach to his religion
would be similar to Hinduism. Julian, of course, derived it from Greek philosophical notions. Specifically, from the way Neoplatonism had given a religious reading to Plato's theory of forms, leading to an idea of there being some "highest level of reality", where the Good and the True and the Just and the Beautiful would all be indentical and united in one divine Absolute. (Which also tied into philosiophical notions of a Monad / First Cause / Unmoved Mover etc.) At face value, and in the basic shape of the concept, that
is pretty similar to the Hindu notion of
Brahman, and the way Julian viewed the gods in relation to the Neoplatonic Absolute is indeed a lot like the way Hinduism views the gods in relation to
Brahman.
In that particular context of Hinduism, one might argue that the old
Religio Romana was like the Vedic religion, which would make Julian the initiator of
Vedanta: rather than the one restoring the old ways, he'd be capping them off, and beginning a whole new chapter. A whole new book. A whole new religion-- rooted in the old traditions, yes, but ultimately something wholly new and different.