Actually I tried to do exactly this. Except the gopro webcam software straight up doesn't work and they don't plan on fixing it.
Its depressing really.
That would indeed put a dent in that plan :\ I suppose there are always DSLRs, as those are also sometimes in a similar price bracket (many recent ones can act as a webcam as well).
I gather support / fixes / etc have been rolling out rather slowly, have you tried it in the past few months? Or is it currently that unusable? I certainly wouldn't expect the software to be difficult to build, there are quite a few webcam-emulating projects out there... but then again this is a company's software rather than an interested hobbyist.