I think Michael would not have killed Carlo until Vito died. If you notice, Michael didn't do anything drastic until Vito died. I believe that as long as his father was alive, he thought that Vito would always be breathing down his neck, making sure Michael never messed up. Even though I don't think Vito was trying to supervise him-we learn that he does support whatever Michael does when the whole "Tom-your out" scene takes place-but I believe that Michael was so independent, he couldn't really go head strong until he knew he wouldn't be judged.
Maybe that was his way of making sure he would never disappoint his father, as we all know Michael tried his hardest to live up to Vito's expectations and rightfully so.