I suppose it might become more Hellenized, indeed. Not sure how this reflects in politics, but in the cultural (perhaps on surface level, like fashion trends, cultural idiossincrasies and eccentricities) we might witness a pronounced influence of Egypt/Syria. An earlier "Orientalist" trend, if you may, like it happened in the reign of Elagabalus.
Perhaps we even get a "Egypt craze" that allows for more pyramids in Rome. Besides that of Gaius Cestius, of course (
https://en.wikipedia.org/wiki/Pyramid_of_Cestius)