I can say, emphatically, YES. Shaved bats hit regular Clinchers farther, let alone Clincher Golds. I've been playing in Clincher modified leagues for 15+ years. Clincher Golds are just a step below a "regular" softball, imo. They are markedly better than the F-12s. So much so that all my leagues went to the F-12s, from the Golds, years ago for safety purposes.
Mush ball is a relative term, imo. If you've held a Gold and a 52/300, side by side, the 52 is harder. However, the Gold is hard but has the thicker leather cover, so it feels softer. The ball will still compress the shell of the bat for that trampoline effect.
Every team in my modified leagues have shaved bats and you can tell when the ball is hit. It definitely will make a difference.
The whole "swing the heaviest bat" theory was good for metal bats. But a composite bat will hit these balls farther and it's not even close.
Ask any of the NY players on here what bats are being used. 99% will say composite.