Maybe the car can be driven away for once. The engine immobilizer requires the keyfob to be present inside the car for it be driven away. If the spoofed fob can trick the immobilizer, yes it can be driven away for once because the immobilizer check is not always "on". Its checked before the engine starts.

If it was, I could throw my keyfob out of the window on a highway and the car would come to a stop.