OSP? I see you are a man of patrician tastes.
I could see the Apollo cult taking on aspects of Christianity as well. Forgiveness? Apollo forgave Hermes for stealing his cattle in exchange for music. Protector of the faithful? Apollo helped his priest in Troy get his daughter back by unleashing a plague on the Greeks. Punisher of the wicked? Not Apollo exactly but among the pantheon there was an underworld court that judged people's souls and there are several stories about Apollo punishing people. What do you guys think?
I also find the idea that Christianity is destined to become the premier European religion to be too fatalistic. It will probably be firmly entrenched in the Balkans and might spread throughout Eastern Europe, but it's not a given that it spreads in Western Europe, especially if the state is promoting a religion that's equally viable and more familiar.
It would take time and effort (the Sun religion would need to be codified with a holy book and rites somehow before anything else), but it is possible.
Well, if you're going with the Hellenic interpretation of the afterlife (Which isn't so different from what I've gathered about the Jewish interpretation... though its a bit of a headache to actually get a straight answer on the later), punishment is generally reserved for only the most wicked of the wicked: your average Joe is destined instead to become a mostly amnesiac shade just sort of... existing in the boring foggy caverns. The Elysian Fields are probably going to have to be depicted as a little more... achievable (Maybe the idea that those who fulfill a "convenient" with Apollo in their mortal lives will get a ride there on his sun chariot when they die as his part of the deal? It'd fit into the more "business arrangement" model that the Romans had with their gods, maybe shifting towards some Wodan-esque influences as it gets adopted in the West due to the greater presence of the Germanic rather than Semetic cultures in the region). Thankfully, though, codifying the faith would be fairly easy to do: the Romans have a great deal of records of their own gods, due to their penchant for writing things down, and fairly easy access to and (general) respect for the Greek cultural mythos (Including the dramas, to get supplementary stories and with the added bonus of being usable as an evangelical/educational tool for the illiterate. Apollo will probably end up being a little more... taciturn than Jesus (Or maybe some of his harder elements get peddled off to other deities in the pantheon, like Hades for unmerciful justice or Artemis for punisher of the wicked; on the balance the religion is probably going to lean towards something closer to a mixture of the Old Testament and the old Roman cults)
i guess that a religion that said "Render unto Caesar the things that are Caesar's, and unto God the things that are God's" is quite appealing to a ruling class, who basically gets the right to rule their subjects during their earthly life and leave them the confort of becoming God's subject when they die. so I guess that, politically speaking, even if he saw Apollo or anyone else, good old Emperor Constantinus would probably "mistake" him or her for Christ or the Virgin Mary
... which is a message the old Hellenic-inspired core pantheon wasen't exactly alien too. Indeed, humility and reverence to authority were key parts of the Roman religious system (Remember, huberious was the most common fatal flaw in the folklore). Indeed, its generally part of any hierarchically-structured religion