Git exposes a lot of internals through odd commands, so I suspect you could manage synchronization by sending changes over email or something.

Bonus fun fact: there’s a git bundle command that “dumps” the repository into a single file, that can be interacted with as a remote. So if you’re ever working with a local repository and want to put it on a server over ssh or something like that, you can just create a bundle, scp it over, and clone from that on the server.