It does, and I did try it for a couple of years — I even ran my own server. None of my close friends cared to try it, and I preferred XMPP myself, so I took down the server and delete the app.
tcfhgj
It doesn't. I don't know how you can deny it at all, it's core Matrix functionality.
Even WhatsApp has sync by now (even if it's artificially limited and works differently).