No. If the moon did not rotate at all we would still see the same visible "fraction" of the moon's surface.
At the full moon phase we would still the entire surface of 1/2 of the moon regardless of which side of the moon we were observing.
Actually the moon does not make one rotation for each revolution of the earth, but rather, one rotation for each complete revolution of the moon around the the earth. That's why we always see the same side of the moon from earth. The back side of the moon is never visible from earth.
