On Android, your local library and your mixtapes play fully offline. The files are on the phone, the player is on the phone, and nothing needs to phone home to start a tape.
What needs a connection
Internet radio does, because it's a live stream. Online lookups for cover art and tags do too. With no signal, they won't work until you're back online.
The purchase check
Audionix checks with Google Play when it opens that your account still owns the app. If you're offline at that moment, it carries on. You can use it anywhere without worrying about being locked out by a bad signal.
Before a trip
A good habit: queue a few tapes or build a mixtape before you leave. They'll play the same on a plane or in a tunnel as they do at home.
Saved radio stations are the exception, since they're streams. Keep a folder tape or two handy for the dead zones.