Ohhhhh damn, that stinks, Todd - sorry man I've had bolts about that size snap off a copule times when trying to extract them from motorcycles after high speed crashes where stuff was bent and I did (eventually) manage to extract them, but it was a BEEOTCH. They were also not that deep, but broken off at the surface, so I would have to think that, plus being underneath the car would make it pretty tough. I can't imagine you would hurt anything by driving it somewhere. I think I would if it were me, FWIW. Good luck, man!!
BTW - did you determine if it was actually necessary to loosen those bolts or not? Was the install fairly strait forward aside from that? I have the Tyrol kit sitting on my shelf (+ some other stuff) that I have not felt like crawling under my car given the heat / have not had time for yet, and have been debating having them done at a shop vs DIY.