I believe that you are correct. He will not qualify at either position. I've seen this in one world where a particular player was split at around 45 games each at two different position. I believe it was also SS and 2B, as in your case. Overall offensive and defensive numbers dictated that he was clearly better than any of the four selected SS's and 2B's, but he wasn't on the roster.
Don't know what the cut off for number of games needed to qualify would be.