Alpine Flyer
I Can only reference the 737, for which as far as I recall a cat 3A autoland can be flown with the auto-throttle inoperative, or at least you can continue and land if the auto-throttle fails, I can't remember if you can commence the approach with it inoperative, but I think you can.
On the 737 with HGS both auto-pilot and auto-throttle are disengaged at or above 1000 ft above the airfield for cat 2 or 3A, and the approach is flown entirely manually. Whether that is sensible at the end of a long night is questionable, but that is the procedure.
As for the Q400, the SOP has obviously changed since I flew it as the Captain used to fly the approach and landing, or maybe the F/O flying is a flybe thing. Most of the time for cat 2 conditions the atmosphere is fairly stable, I don't remember any issues with thrust lever response, and I flew a fair few actual cat 2 approaches in it, and taught them in the simulator.