This might sound dumb but what does the boost bypass do?

 

It stops the car from bleeding the pressure when you have a smaller pulley

 

a bypass valve that eaton uses on its roots blowers is a valve that opens and closes to control boost. It works off a Throttle Positioning Sensor, when low throttle is applied the valve opens and lets the boost pressure caused by the supercharger to be vented into the atmospher rather than into the engine, this saves on fuel economy. When the Throttle is pushed heavily, the valve closes and directs the air into the engine, improving performance.

It has nothing to do with pulley size

 

Look in the videos, I think there is one that kinda shows it.