I would assume github could supercede your license by putting its own claim to your code in the TOS. I doubt they have done that, but just pointing it out.
Sure they can, search engines produce copyrighted material all the time. The issue comes in when people think this somehow indemnifies them as users of Copilot - my guess is, it doesn't protect you any more than if you use a search engine to copy an entire codebase for your own purposes.
It would be also the end of GitHub, as most users probably won’t accept such terms.