I'm not entirely sure.
She might have an easier time of spreading Heliosianism. The chauvanism of Ancient Greece would probably have made it about as difficult as the original Dawnverse for her to establish a female primogeniture based system.
There wouldn't be a rival organised religion to oppose her though so Heliosianism would have psread even further and then probably undergo some kind of schism, probably perpetrated by figures similar to Apollonia II.
Potential rivals for Caesar's Rome: (Parthia, some kind of Germanic Confederation)
Potential rivals for just before Alexander's Conquests (Carthage, Mauryan Empire, some kind of Gaelic Confederation)