there is always the possibility that he could throw it at you. (silly question coming up) is he vindictive like that? i mean, it would be one of those - he couldn't really prove it, but they guy did stay there. but you really couldn't prove that nothing didn't happen either.
alot would be with the age of the child. is he old enough to know that your friend is just staying over until the apartment is ready? or is he younger? will the wife who kicked him out cause you any problems? will there be fighting and any "scenes" in your home in front of the child? you are getting into the middle of a domestic situation - you can't really tell what it would be like. they are liable to fight, argue, carry on. how much do you want your child to see. do you want to take the chance that it won't happen.
my lawyers favorite quote - "if it looks like it could hurt you in ANY way, don't do it."
if you think your ex will throw it up at you, your friend should understand if you have to back out on your offer.