You could easily use a send-email/am workflow with a github repo. It'd be identical to using your own git remote.
It would also be possible for github to add a email@example.com that accepts a send-email formatted patch mail and creates pull-requests.
The only reason these don't happen is because nobody really wants that. The first one is immediately and completely possible, but you'd get harrassed by all the people that want the pull request UX. The second would require effort on the part of github in order to please an audience of nearly zero.
Edit: Honestly I think you'd get just as much grief from the people who want pull requests when using a private repo ("Why not just use Github"), except maybe that they don't know your project exists. It's up to you if you want to care, regardless of where your remote is.