When I go over my data limit I can still play, slowly.
It usually takes a few tries to log on, and when changing worlds (going in/out of a house) it can take up to three minutes for objects to load.
During that time however I can move around and interact with the objects already loaded.
It just happens that the crossroad I use most, is ALWAYS the last object to load
When I'm out of data I never go outside the walls on a character I mind losing, since on the odd occasion a tree or a rock or even a person doesn't get loaded until I've walked past or into them.