That's happened to me twice in panic situations, long ago. Your heart stops for a split second, but, as long as you remember ( or have a reflex ) to let go of the rear brake, you don't go down.

I still use the rear brake when I need to stop quickly, because until you hit the point of actually lifting the back wheel, it's doing something to slow you down. But some quick stop drills helped me train myself to mostly pull with the left hand when I want to stop in a hurry.