[750hp]

Guys have had problems running a cog belt on centrifugal blower without a big enough bypass valve. As you get off the throttle for a gear change, if you can't dump all of that compressed air immediately it can reverberate back to the blower. As the cog belts don't allow some slippage like a serpentine belt, this can lead to them shearing teeth in higher boost applications.
Decent bypass valve solves the problem completely.

To answer your question - supercharged engines don't hate gearboxes, but most driveline parts will hate the power of a supercharged engine if they're not designed as part of a complete bulletproof package...