Either Mesopotamia-scale, or definitive Upper/Lower Egypt division (no, "It was OTL : Intermediary Periods", please), would have it been possible to have a politically (and possibly culturally) divided Ancient Egypt?
I suppose being more prone to foreign invasions would be a huge factor, but I'm not sure it would be enough (critically giving that Egypt was invaded several times).
The OP isn't about not having regular cycles of unification, Sargon or Hammburabi-style, but Ancient Egypt should be associated ITTL with at least two distinct entities (that doesn't have to be the same).
Eventually, what would be the consequences? (Giving the butterflies, I'll spare you "up to nowadays", let's focus on relativly immediate and regional consequences)