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.