To enter VRS you have to have near zero forward airspeed and a descent rate of about 500 fpm or more under power. Note that VRS is not "settling with power" regardless of what the FAA says - they are two different phenomena. So in practice you would never encounter the conditions that could create a VRS in the first place while autorotating because you normally autorotate with substantial forward airspeed if you want to be able to land in one piece.
But say if you were autorotating, then slowed to zero airspeed so you were now autorotating straight down (and the descent rate goes from holy crap to oh my god), and then you pulled pitch to arrest the descent rate using rotor inertia. Could a vortex ring state be induced during that brief interval? Perhaps one could start to form in that brief few seconds of inertia-generated downwash, but by then the rotor would be stalling and you are now an anvil, so the point is moot.
However, for the purposes of our just-for-fun theoretical discussion, I think that if you had enough rotor inertia, it would be possible theoretically I would say, because for the purposes of the time interval involved, it would be the same as having engine power. Maybe if you had a rotor with super duper uranium tip weights that could generate inertia lift for say 10 seconds or more.
Watch this video to see how fast the vortex ring state can form in a vertical descent with power