It depends, really. Some "Gods" are sometimes concepts really, no real forms. While gods such as Kratos (which he's just a human, so Ben wouldn't be able to become him) and Heracles get their powers from "Trials," and blessings by other gods, so while Ben could become the species of a god (if they are different from human, at least) Ben wouldn't have the powers from the DNA source, since they are gifted upon them, rather than being a natural ability like most aliens.
