My understanding is - if the engine is running and the keyfob moves outside the range detectable by the car, you will get a warning on the dash however the engine will continue to run (believe this is actually a safety feature). If you then stop the engine with the button, you cannot restart it until the keyfob is in range again.
What I'm not sure of is what happens if the keyfob is out of range and ASS stops the engine. Does it restart in those circumstances?
340i in Estoril Blue