I don't think Rempe would have made much of a difference. In the 1st period, they looked lazy and weren't skating with any purpose. Rempe would have possibly made more of a difference in Game 3 when the 'Canes were getting chippy. That may have stopped a bit of that stuff. In Game 4, less chippiness and less penalties.
We'll never know if he would have made a difference since he didn't play. At this point it is all conjecture.