Clark
what do you mean by "app can work"?
A. installing an app => will work pretty much 100% of the time without granting network permission
B. running an app => will work for the vast majority of apps without granting network permission
C. using an app => will heavily depend on the specific features that require network connection
- the sole purpose of the app requires a network connection
ProtonApps: ProtonVPN becomes entirely useless without network connection, like any VPN app would. They literally have network in their name.
- core functions of the app require a network connection
AntennaPod: sure, you can download your favorite podcast first and then deny network permissions after. But that kind of turns your podcast feed reader into a media player app limited to play files saved locally. Quenstionable at best.
- non-essential functions of the app require a network connection
e.g. VLC: yes it can connect to a web radio stream and play it on your phone. But this is probably not the reason why you have it installed. VLC might request network connection but will perform most of its tasks perfectly fine without it.
- no functions of the app require a network connection
Calculators, Clocks, Cameras, Voice Recorders, Note Books, Keyboards, eBook Readers, Contact Books and Calendars: In my personal opinion, these apps do not require and therefore should not request permission to connect to networks. And if they do then they either a) harvest your data or b) include functions which are stupid, like scrobbling what you're currently listening to on your music player to last.fm/libre.fm.
TL;DR : " i t d e p e n d s " and you will have to individually check on your own. on f-droid many apps that require not network connections will have "offline" as part of their name, e.g. "offline calendar"