Personally I wouldn't come clean. It might make him think you are the type of person who is willing to tell white lies. Now don't take this the wrong way, we all buy reps, we're all living the lie He thinks it gen so run with it. He is very unlikely to spot it is a rep, and why would he have any reason to think it isn't a gen. This is merely to clean your conscience. Telling the truth in the first place would have been the right thing to do, however admitting it now might be the morally right thing to do, but it doesn't mean it is necessarily the correct decision to make.
You can also still open up to him about reps. Many people, myself included have gens and reps, it's nothing out of the ordinary. I am pretty sure he couldn't give a damn whether it was a rep or a gen, and in going to him and admitting it is a fake, he might think your indecisive (not knowing what to say and then changing your mind), and that you might be covering other things up.