It should keep working exactly the same way it does with a connection, since a lot of industrial work happens in places where signal is weak or gone completely, like remote pads, offshore decks and the inside of large plants. An app that needs a connection to open a procedure or save a step will simply not be used in those places.
Offline should mean the procedures, forms and recent data are already on the device, every step and capture is saved locally while the job happens and everything syncs once a connection comes back. The Interface mobile app is built to run offline for this reason, because the field is exactly where the connection is least reliable.