I bet if you removed the belt from the supercharger and you grabbed the superchargers pulley and move it back and forth quickly you would feel alot of slack and that where the rocks in a bucket sound comes from.
The coupler is a just plastic and over time it wears out and makes that noise.
As for the car stalling/dying, it has nothing to do with the supercharger. Yes the supercharger does spin faster than the engine rpm because the pulley is 1/4th the size of the BIG pulley called the harmonic balancers that spins both belts at the same time. Its purpose is to spin faster and create boost for the car.
Does the car just die out of no where and you are able to start it up and keep going???
Do the rpms drop to zero, then the car dies a short time later?
If so that is a common crank sensor issue.
