Unless I was to add the religion to the game, no. Where the history diverts is way after Rome becomes Christain, so it wouldn't make sense that they suddenly went back to Hellenistic. Although it would be cool.

You could have Julian the apostate be the alternate history focal point. He ruled 361-363 and would by all accounts have succeeded in bringing back paganism as the majority and state religion had he not been killed by an infected wound on a campaign in Persia. Lots of scholars (Gibbon among them) have Christianity as a major dividing factor in Rome, and set it as one of the main factors to its downfal. It's not unthinkable that the nostalgic Julian after a long rule would've set Rome back as a republic. It's definitely a plausible alternate history.

I dont think it would be a good idea to let Iulianus II turn the whole empire back to Hellenistic compulsorily... He would eventually ruin the empire because the most of roman population at that time was already converted to christianity and Iulianus II had actually already destroyed the administrative system built by Constantinus the Great before he got finished during the war against persians (which actually caused the fall of western half of the empire, Theodosius the Great had successfully restored the the administrative system of the eastern half, he tried to do the same in the western half but eventually died too early in Mediolanum(called Milan today) to make it). Maybe for a better alternate history we should let Pilatus banish Christus and his 12 Apostles to Far East or somewhere else mega far away from the roman territory instead of killing them :).

i love how god wants to kill himself

also roman specific christianity when?

I think Orthodox would be more appropriate for Rome. Byzantium is basically the eastern half of the empire, and it is orthodox.

The schism happened after the fall of the Western Roman Empire, so it makes sense that if the WRE survived, there could still be a schism and the west would remain Catholic and the east Orthodox