So you’d do peer-to-peer networking using WebRTC? That’ll definitely require JS, and seems pretty complicated. There’s also no real safe way to store data in a browser (that survives “clearing cookies”).
I think the simplest option when you don’t want to worry about the backend is probably a BaaS like Firebase. With Firebase you can get realtime messaging too, though you’ll have to install the Firebase JS client and connect it to Elm with ports.