Greg and I discussed this a few weeks ago in the office.
In the UI for the active, logged-in account, what we care most about is whether the app can reach the specific Zulip server. We care less about @react-native-community/netinfo's interpretation of whether the Internet is reachable in general, from information given by the OS. In fact, this proposal was prompted by what seems to be at least one bug in @r-n-c/netinfo where the notice ends up flickering back and forth on Android. Possibly a VPN is involved when that happens; anyway, we should remove our exposure to such bugs.
If we get a network error from our event polling, we should let the user know that we've had trouble reaching the server. We should think about how to decide as soon as possible that we've recovered from that state.
(More details TBD; filing as a placeholder.)