That's not how git works... Yes, you can have remotes where you pull your initial state. You can have many remotes -- any git repo you've cloned can be used to host the repo publicly. But after that, you can merge patches that people send you over email (or heck, even via carrier pigeon), do everything you need without a host. In fact some people have made a github-like hosting solution that is decentralised called GitTorrent.

But which one does the team deploy if everyone is sending patches to each other.