Not too sure it'd do much on a supercharger, but the idea on a turbo is to stop the built up pressure running backward thru the turbine and, in turn, spinning the turbine backwards and causing undue stress on the turbine wheel. It is wank factor for a lot of ricers, but, it all depends on how big the turbo is too.
The BOV is to stop reversion, a bit like shock waves from the air flow slamming into the throttle plate.
A BOV will sort the problem and maintain the turbo rpm through gear changes.
You need to check your engine management though. If it's AFM based, you'll need a plumb back BOV.
MAP sensor based engine management could vent to atmo.