Surely you would have anticipated such conditions and set-up for an autoland?
Personally I brief autoland if any significant cloud below 500ft or vis less than 1500m and consider reverting to Cat I if appropriate. Can't go the other way though, and its a bit embarrassing to explain to the CP why you had to go around in a CatIII equipped aeroplane just because you hadn't set it up...
Boeing 737 & 1 autopilot. "technically"... Hmmm, well, yes, it will autoland fine with just one but there's no redundancy so not exactly a sensible thing to do unless you're going to die otherwise. You "could technically" do all sorts of things in any aeroplane but that's a pretty pointless line of discussion really.