Apps fall into three groups: those that store data locally and sync later, those that cache a copy for reading, and those that are just a window onto a server and stop working entirely offline.
Trouble usually arrives at the boundary. A half-connected network — signal present, data not moving — is worse than no connection at all, because the app keeps waiting instead of switching to its offline copy.
Sync conflicts are the other risk. Edits made offline on two devices must be merged later, and not every app handles that gracefully.
Downloading maps, documents and media deliberately before travelling avoids nearly all of it.