As we know, when the Roman Empire was whole (i.e. a cohesive single polity
I'm not sure that defines the Roman state very well, at least ideologically. Roman imperium first concieved itself as a form of hegemony on steroids, whom the addition of municipal liberties under Roman protection formed the backbone of most imperial institutions (if not Roman in the strictest sense).
While it was cohesive (at least up to a certain point), it was still an mosaic of various features that admittedly went trough more unification with time but never at the same scale than, say, China, not until the IVth century in the West and the VIth century in the East (roughly, the disappearence of municipes as a main institutional feature).
the peripheral peoples were tribal, nomadic, and anarchic.
This is as well, I'm afraid, untrue. From rheinish leagues to Mauri communauties, the norm was rather the more or less integrated peripherical entity (in the case of Mauri for instance, being largely integrated into the provincial institutions) labelling these as purely tribal, nomadic and anarchic is flat out wrong would it be only because the mere presence of Romania (and the structuralizing influence it had) created most of Late Antiquity political identities in the periphery of Romania.
State isn't contradictory to tribe (archaic Roman state was largely based on tribal features, for instance) and their structuration is largely due to an outer perspective and influence on an already established body based on kinship. You could make a case about how Welsh petty-kingdoms largely paralleled old tribal denominations.
That said, "pure" tribal identity, if not contradictory, isn't the same as a state/popular identity mostly because the sense of kinship on the later is more broad, less clear and being based much less on common experience than social differenciation with an elite becoming a key factor in transferring, trough power accumulation, this sense of kinship.
Anarchic is, again, a weird way to see this : because we can differenciate an elite among peripherical peoples (especially in their relation to Rome, which both translated and established an hierarchy based on its own concepts : Mauri "dukes", Germanic "kings", etc.)
As for nomadic, you have at the contrary quite well established territories (in comparison of the hinterland) for what matter the periphery of the Barbaricum : even before foedi of the IIIrd century, we know where Marcomanni peoples lives, or where Gothic people lives in the IVth century. These, as peoples emerging from a fusion of various elements, were relatively stable territorialy : the whole
Völkerwanderung narrative may look nice on paper, but virtually all of the Barbaricum peoples began to exist as such in the IIIrd century along Roman periphery (not to say that you didn't have more or less important migrations in Central Europe, but these weren't migrating
peoples).
You could make a case about how, even disregarding the pre-IIIrd century recits, peoples as Goths managed to move from Danube to Spain and Italy. It would be a good point, but you'd notice that these manage to survive as a landed people nevertheless, thanks to their integration into Romania institutions (or other Barbarian groups, such as Alans), especially the military which had an important part on late Roman identity (including administration).
I could agree with further you go from Rome, more chances to have people being less determined (objectively and subjectively), less stable and overall "simpler" institutionally (even that would be subject to discussion tough) but for what matter people directly in contact with Rome, it strikes me as an archaic viewpoint.
The collapse of the Roman Empire allowed many of these tribal peoples to adopt Romanesque models of rule and control, which then allowed for the establishment of cohesive nation-states in Western Europe first and Eastern Europe next.
Rather than adoption, it's more of a continuity of Late Imperial structures in both west and east : a continuity on a clearly more fragile base (disapperance of Roman state in the West, social/economical decline in the Est some time afterwards), but most of peoples in Romania by the Vth were already importantly romanized (would it be only trough previous integration, and because a lot of these people were actually Roman to begin with).
In fact, the late roman
militia (the military and civil organisational model) declined onwards (if not continuously) in spite of Romano-Barbarian rulers efforts : it depended too much of a strong fiscality (even if the direct service and honores given by the king did helped a bit), the growing mix between landed elite and bureaucratic elite, and more or less based on the need of hegemonous authority rather than imperial authority over the ruled regions.
It was a model, no discussion, but a model hugely adapted and concieved along the social-political situation of the time (as in, the rise of regional aristocracy on palatial aristocracy). Not before the reintroduction of late imperial Roman law on matter of states, you see the reappearance of noticiable bureaucracies in Christiendom (for what matters western Europe, of course).
The late imperial structures played no role into the appearance of nations-states (which, if we're generous, can be traced back around the XVIIth century), even if the Roman model (half-fantasied) did inspired and allowed its IOTL appearance.
See Servir l'Etat Barbare dans la Gaule Franque, Bruno Dumézil
My question is this; if Rome did not collapse, or if a successor to Rome, such as Francia, succeeded in conquering Roman territory once more, would be the fate of the peripheral tribes?
I'm myself, rather a proponent of Service, Renfrew or Collins ideas on the development of state. I'd think that the maintain of a proper imperial structure would have the same effects than IOTL Carolingia or Byzantium on Slavs, as in the appearance of early states thanks to imperial influence and political support of such entities (even if not-concious).
Simply said, states are like dose : when you have some, you want to share it as much as possible.
It's easier to manage the barbarians at the border when you have six tribes on your side and four against you, for example.
I'm not sure that's a good depiction of the situation : not only tribes aren't a synonym for people (tribes, again, are first based on a clearly established kinship and trough relative undifferenciation between clans, at least ideally), but it's less about number than how integrated they are to an imperial structure. For exemple, poorly integrated politically (but integrated culturally and socially) peoples can bit you back in the ass quite easily (see Ostrogoths send by Constantinople over Italy).
Eventually, I think your vision is a bit anachronistic : Rome wasn't really a nation-state, being much more based on imperial/palatial identity from one hand, municipal/urban from the other. Romania eventually included an awful lot of defined peoples : even not mentioning foedi, you still have the lot of groups as submitted nations, laeti, more or less integrated peoples as Mauri, peripherical cities, etc. What gathered all of that wasn't the sense of people being all Roman (or rather, being essentially or only Roman) or being part of a same enlarged kinship (which is an important part of national identity), but the omnipresent sense of homogenic political identity.
One could be Frank or Narbonese from birth and from kinship, but a Roman citizen.
And tribe can gather so much different sense that I think we really have to stress a clear definition : an human group with limited social distinction and a sense of common kinship trough ancestry (Michat Timowsky). Do we agree on it?