CAT3 is landing on under extremely poor visibility conditions where the aircraft is setup for autoland, the pilots can once they have acquired the runway take manual control. But at CAT3 you are typically looking at situations where you might see the runway at 50 feet

Had a foggy landing to Milan recently and we got the full routine of devices off. Everyone has probably heard the breakthrough on a radio of a nearby mobile phone, the frequencies used by part of the system are very near to standard FM radio, so you can see why they get serious about switching things off

I only had one confirmed autoland in ~500 flights and that was Dublin on a clear evening for training/aircraft currency, the tell tale being the landing was extremely smooth and the auto pilot disconnect warning could be heard just as we came to a halt on the runway. The autoland after landing will use the rudder to keep the aircraft rolling down the centreline of the runway. Obviously in training where you can see the runway any issue would result in immediate pilot intervention so you don't need to go through the whole process.