Sure, why not?
I don't know much about the Unversed, but as I understand it they really only make sense in the prequel game. Best to stick with Heartless and Nobodies. Makes the RP more accessible to those who've only played KH and KH2.
There's some important questions to answer here, though.
1) Time period. Does this happen before or after the games? During is also an option, but it'd be trickier.
2) Keyblades are pretty important to the story. Is any character going to be allowed to wield one? Or are we going to limit them?
3) How many people are you even going to let in?
4) Do you have an idea of who/what the main threat is already?