It's not a SPA that can run without a backend, so no. Most of the clients will need to connect via the backend which is currently run at wss://snapdrop.net/server/webrtc. Without it, they won't be able to penetrate NAT and will be unreachable.
You and many others :) WebRTC (Web Real-Time Communications) is faux-P2P, in that in order to establish the P2P connection, you'll need a server in-between as browsers cannot accept incoming connections, you can only dial out and then start listen for replies.
> If a server is needed anyway, could it be implemented in easier, OpenWRT-compatible way?
I'm not sure why it would have to be OpenWRT-compatible? OpenWRT is just Linux run on less-powerful hardware (over-simplification obviously), so anything Linux can run, should be able to run on OpenWRT. Find your favorite STUN/signalling server and try running on OpenWRT, should work fine.