Interestingly, I was just pondering the same question.
It really is hard to say. A lot of people don't think Jesus would even be born. But I'm willing to bet that there would be an analogue, a Jewish man with similar thoughts who might be seen as the messiah, the promised one, by other jews. There would still be a lot of permeating Hellenistic thought (even Maccabees, the book about how the Jews ousted the Greeks, was written in Greek).
Would this Christ have the exact same theology, likely not. But the circumstances are still ripe for Judaism to evolve a messianic branch. The Hasmoneans were very corrupt, and could be seen by the people as traitors to God, or the people, or any myriad of reasons. Historically, the people of Judah were rarely content with their rulers, but then again, they rarely had good rulers. You have several Jewish sects that would be present and would influence the christ analogue (zealots, pharisees, scribes, hermits).
if this pseudo-christianity catches, it might be seen as a threat by the hasmonians, the christ-figure executed, and the pseudo-christians are forced into either exile or persecution from the state. But in order for this christianity to be something different than just another jewish sect, it needs to convert. how well they do so depends on the world outside judea.