It seems that there is an automated process that can result in questions getting tagged as untagged, but it should not be possible for users to generate questions with this tagging. (The example is from SciFi.SE, but I think the rule should apply network wide.)
If no other mechanism exists the moderator only tag mechanism could, perhaps, be made to serve here.
Side question: should untagged be allowed to users on meta site? Or would it be better to use untagged-questions to for questions about question tagged untagged?