What's the use case you had in mind? Running offst as a daemon on an average 8h-a-day workstation/PC/Laptop? Or on a server? In any case, a mobile phone is basically offline most time -- It seems to be online thanks to push-services like the Google or Apple cloud ones, but that API is hardly usable for offset without some kind of relay server (however, you do have relays already in the design, which is neat).
However, running a networking service (daemon, app, whatever you want to call it) 24h on a mobile phone will massively drain the battery, just because Wifi et al needs some power.