Neo-Platonic religion is probably a good indicator. In other words, they would have reacted to Christianity by becoming highly syncretic and fusing a philosophical system to the outward forms of religious expression. They also would have come to consider themselves a single tradition with many facets, as opposed to a bunch of entirely independent, localized cults, becoming somewhat organized in the process. They probably also would have become more interested in humanistic pursuits and social justice and eventually moved away from the sacrificial model of practice. In other words, they would have imitated Christianity just far enough to really compete with it, while keeping their own diverse character.
Hellenic religion in the form of Neo-Platonism (which actually included religious traditions from Egypt, Syria, and other places, despite the name) became a pretty robust tradition by the end, but it was too little too late, and there was already heavy state oppression from the Theodosian period onward. All modern paganism is heavily influenced by the Neo-Platonic model, even if its practitioners don't consciously realize it. It was the very first neopagan movement, in a sense. The thing is, it didn't survive long enough to take traditions from Northern Europe under its wing, though it would have been happy to do so. As far as they were concerned, "Hellenism" was the native, non-Christian traditions of any peoples whatsoever. Basically, it took Christianity for the Greeks to suddenly realize that all the religious cultures around them were hella awesome and needed to be preserved against the oncoming storm.