That's right. Git as an offline cache. When you read a peers message, you can also update you own git repo to say you read it, and so when the peer comes online they can update their side to delete the messages (keeping the size small)... Going further against the grain, the app doesn't care about the history of messages deleted, so I expect to add things for purging history.
I considered the Blockchain, but i think the git approach is better. It's hard to describe what I'm imagining. I'd like to put together a demo when I get time.
I have a full-ish description of the protocol.
https://positive-intentions.com/docs/technical/whitepaper/complete-protocol-spec
Instead of reading that, if you really want to know more, I would suggest you ask me for clarity. (Nothing about this git approach is mentioned there.)