Quite possible, based on my experience. I wanted to reduce the grip size on 3/8 tfight320s and removed the original grips and, not long after, the top of the handle started squeaking, rattling, and feeling unstable on each of the racquets. I use screws and superglue from time to time, but the fix is always temporary. Perhaps the original grip is part of the basic handle infrastructure on some racquets.
i don't remember