Out of curiosity I played with the E parking brake on my wife's Audi. It doesn't "set" while moving, it goes on for a Second, then turns off again. It will however stay on if you continue to hold the button, so it does function as an Emergency brake. Final point, It is not strong enough to lock the brakes or anything, but it does provide some decent braking.
'65 A-code coupe, T-10 4-speed, 8" 3.25 limited slip