Mesopotamia is close enough to Palestine that the diverse strands of the evolving doctrines might all get absorbed into a Buddhist framework, maybe. I rather think, especially if we can take Acts as any sort of shadow of the historical truth of events in the generation after the Crucifixion, that it spread far and wide pretty fast--if not appreciably far into the west (Italy and beyond) then anyway widely in the Greek zone in the east, to eastern North Africa (Cyrene) and all over Anatolia. And this was well before Trajan's conquests OTL. By his time, it seems reasonable, unless Acts and the letters of Paul to various destinations are all made up centuries after the fact (as I suppose may be but even as an agnostic I feel these books read like authentic documents of their purported times, though I'm no modern Biblical scholar and someone might have proven long ago they are not) that the number of professed Christians, perhaps of very diverse beliefs, in Rome itself was substantial. All of these people scattered all over the eastern half of the Empire (as it was prior to the annexation of Mesopotamia) seem out of immediate range of the Buddhist influence as it were. That is, some of them can still be drawn into that interpretation, especially in Rome itself which draws all things to itself in this era.
But instead of thinking it plausible that the OTL range of interpretations of Christianity would be absorbed wholesale into a Buddhist influenced one, I would think it would just add another branch to the tree. A branch that might be very very substantial, especially on the somewhat virgin soil of Mesopotamia. So it may well indeed come to dominate that set of provinces, since the earlier spread would have been largely within the Imperial sphere. (To be sure these same early sources of Christian tradition also suggest missionary activities spread far and wide outside the Empire early on, south to Ethiopia, north (we know later) among the Germans and other "barbarian" peoples far beyond the boundaries; Thomas is said to have been martyred in India and certainly Christian societies came to exist eventually in Central Asia. Perhaps if I studied the early history of Christianity in Mesopotamia I'd find it spread there quite as rapidly and early as Anatolia. I'm guessing otherwise, that the Persians would have been hostile to it and impeded it but it would spread more easily once Rome rules the lands. So with that assumed delay, an early Buddhist/Christian synergy would have an early edge there.
But if we were to suppose it absorbs and overwhelms all other versions, we'd have to suppose there was something with superior appeal about it for some reason or other. This might be the case I suppose. Even then the questions I raise remain relevant unless the author deems it is not within the scope of what they want to write about. Is it Christianity absorbing certain Buddhist elements, or Buddhism in a somewhat Christianized guise, or some third thing? The answer to this has bearing on what can and can't happen next and what likely consequences are. I'd think in the first case, it can merge into the general spectrum and even if it remains a regional sect that eventually comes under central government persecution, it can still transfer doctrinal, mythic and ritual elements to the other branches. And it can become the orthodoxy and despite some significant shifts in doctrine and emphasis, the ATL faith is still basically Christian. In the second case, its spread over all the empire will mean basically that the Empire goes Buddhist instead of Christian, and presumably some Christians will lurk around here and there in odd corners protesting, or anyway clinging to their own orthodoxies that don't accept the larger Buddhist church. Or it might, as yet another sect of Christianity might, become the peculiar doctrine of the eastern provinces and so come into conflict with central orthodoxy (or force the central imperial powers to adopt some kind of separation of church and state doctrine that seems highly unlikely, cool as it would be from a modern liberal point of view). In the third case--it is beyond my imagination and if the author is prepared to blow my mind, it always does enjoy a good blowing!
So I don't think I did misunderstand, I think the timing is wrong to convert all the already converted Christians and all their potential converts to this new eastern variant, unless there is something really amazingly remarkable about it that causes it to steamroller all other sects before it. Or the Imperium adopts it very very early, which is problematic since most of the powers that be in the Empire would not be ready to convert just yet. Perhaps something that enables an early emperor to adopt it early is that it carries over from Buddhism a relaxed attitude toward literal truth in favor of useful metaphor and parable recognized as such. Such a Buddha-Christian synthesis, that is not also an angry denunciation of "false gods" but a parable of good life and good death and a wise philosophic standpoint, would I would think have left the quest for hard-core, irrefutable Truth of the Abrahamic tradition out of itself somehow and would therefore be fundamentally Buddhist, not Christian, and would in time and in suitable setting drop the Christian elements for the most part and take up other mythic trappings as easily. So it might well sweep the empire, especially if for the moment other gods can be kept around, and gradually displace them.
If I misread it, perhaps I projected that reference to Christian elements would seem familiar to uptime history readers, but perhaps they find these exotic?
If Christianity survives uptime as anything other than records of yet another mystery cult long abandoned, I think it must in a form that would reject being encapsulated in Buddhism like that. It may well be an odd minority set of sects in a mostly Romano-Buddhist metasociety of course.
