What Mono said.
Plus, you guys have a KID. You can't have people moving in and out (either as a dirty pun or otherwise) at whim and expect that to foster a healthy environment for your child. You don't even know this guy. He could turn out to be a child molester, a thief, a mooch, whatever.
Don't do it. If you agree that your wife ought to pursue this, let him get his own place and get to know each other better before getting in a situation that you can't get out of very easily.