I mean if the goverment can see which apps you have installed (can they?) then they probably wouldnt like briar. Briar itself is a very good and secure project, that can still work even if the goverment shuts down internet access. So if you have the option of putting a custom operating system on your phone, then briar is a good solution for anonymous communication.
The offline function is meant for emergency or large scale protest like in Hong Kong, not for normal messaging.
But yes if you have for example a big chat group then anyone who is in that group will share the encrypted chats to other devices in the same chat group that are in wifi/bluetooth range or connected to the internet(also tor network).
The diagram explains it pretty well, but generally in case of a full internet blackout it works very well if you have a bunch of people close together (same building, group on the street, etc). You can also create a so called mesh of wifi networks(not connected to the internet just local network) that spans a very big area and it will work with that.
If you have internet access it works like a completely normal messenger.