Depends on their acting abilities, doesn't it? Pretending to be something they are not is kind of in the job description, and if they can pull off a role well then who cares about who they are in real life?
Just what I was thinking. You get one of the crazy good actors, all is well pretty much no matter what. I'm thinking Tom Hanks, Edward Norton, etc... People where you're shocked to find out that two very different characters were played by the same actor. You get actors who essentially play themselves with a different name every part as well, they wouldn't be good for this sort of stuff.
In between you have decent actors who are trying to stretch enough, but just can't fool the camera.