The bag being full won't stop it. I have foolishly neglected mine for too long a time or two and what happens is that it will fill up solid, like a big brick, but still keep sucking. I have had mine get so bad that it filled the hose, clear up to the tool end! It was still trying to pull in chips, but they didn't have anywhere to go. It took longer to unclog the hose than it did to change the bag.
Speaking of which, I need to check that first thing Monday morning.