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.
"Roddick was better than Djokovic on grass...not all surfaces. That is a reasonable opinion as both have won Wimbledon once" - Steve Dykstra