Like other Tor-based apps like OnionShare or Ricochet, Tor gives us a nice overlay network where every onion address is permanent (it's just a keypair) and NAT traversal is taken care of. So you get an invite link with a few addresses in it and you sync others.
We're also working on an optional server to support notifications on iOS where apps cannot run in the background enough to be useful. We expect a lot of people will use this to improve performance on other platforms too, but you won't need to.
Quiet is still not ready for daily use yet, and not audited, but we're serious about making it useful to small workplace teams and activist orgs that need something between Slack and Signal.
Quiet founder here!
We're also working on an optional push notification server which is necessary for iOS anyway, so that is our fallback if we can't get full p2p battery life to a good place.
But I can already get through a day with it even though we've done nothing to optimize, albeit with very noticeable battery use on mobile data (Wi-Fi battery use is much chiller).
I'm sure we could reduce drain by 3x by being more strategic about when we hit the network. And yeah, typical push is the fallback we're working on for people who don't want the battery drain.