I remember a similar discussion taking place a year ago more or less.
@Gloss and
@SlyDessertFox pretty much already nailed it. Everyone seems to think that the big success of Christianity during the IV century can only be attributed to it being inherently a better religion than anything else humanity came up with. While conveniently ignoring a few points:
a) The IV century was almost totally dominated by Christian emperors;
b) Being of the correct faith could great aid one’s career. We have already seen some examples in this thread and it shouldn’t be hard to link the conversion of part of the elite of the empire with the conversion of the common people. After all those were the people who supposedly were more involved in the maintenance of pagan temple, who now were more interested in financing the building of new churches.
c) The increasing powers granted to the clergy like being exempted from taxes, military service or the burdens of the Curiales, not to mention shared power with the provincial governors.
d) How to many so called Christians, Christ himself was another god added to their own collection. But that was enough to count them as Christians and Christians only.
e) Age of crisis can prompt people to find new ways: after all iconoclasm was just a movement that tried to solve the issues of why the Christian world was losing ground against Islam, and the answer more or less was that the old ways were wrong. And if I remember it correctly during the age of Justinian himself we had a small boots to the Monophysite creed in the heart of the empire itself, Constantinople. Nothing to ensure that the capital would become majority Monophysite mind you, but the plague had challenged the faith of many and led some of them to reject the way of the past.
So to go back to the OP, nope I don’t think paganism was doomed, not with an emperor like Julian living longer and sponsoring it. I’m not sure his reform of the religion would work out well, but him living long enough would go a long way to ensure pagans would remain pagans instead of being forced (or enticed) to convert to Christianity.