She did, but her relationship with Anthony (and Caesar before him) was a lot of political calculus to keep herself in power (as is sort of reflected in her primary agenda) more than just general 'she really liked men'. If they were going to do that it seems more appropriate for I dunno Henry VIII or Catherine the Great? I can't think of anyone in the game off hand, but leaders along those lines.No, not at all. The agenda is merely reflecting the historical reality that Cleopatra had a famous relationship with Marc Anthony.
I remain thinking it's a stupid agenda game mechanic-wise, as it just more makes it seem 'the AI will like or hate you for random reasons'.