Example: I am mining on a Windows computer with guiminer on an onboard gpu. Will assigning more memory to the IGP improve its performance while mining?
It seems unlikely. SHA-256 uses very little memory, so while I don't know a lot about GPU mining code, I would doubt that additional GPU memory would be used at all - I can't think what it would be used for.
But if you want to know for sure - since this is a simple BIOS option, why not just try it both ways and see?