Why should a ducted fan/rotor not be capable of working in autorotation?
I never heard about that and cannot find a reason.

How could it? With a duct around it, would you not have to descend straight
down? And if you did, would the rotational mass of a rotor that small in
diameter, and designed to work at such a high rpm, store enough energy in
free fall, to stop your descent when you applied collective to land?