I can't speak to what most people would do, but I've experienced unintended acceleration before. The throttle stuck all the way open while I was driving a friend's car because he routed the throttle cable improperly after installing a larger carburetor for more power. I had intended to give it full throttle, but only briefly.
I stood on the brakes and didn't let up. He reached over and shut off the key, which locked the steering and put us in the ditch, but at relatively low speed due to the continuous braking.
No, and I haven't driven a car with that behavior. Most US market cars have a sequence of lock, off, accessory power, on, start as the key is turned farther clockwise. Some cars require manipulation of a lever near the key to reach the lock position.
Very new cars with an entirely radio-based "key" might behave something like that.
I stood on the brakes and didn't let up. He reached over and shut off the key, which locked the steering and put us in the ditch, but at relatively low speed due to the continuous braking.