I'm completely rewriting my answer since in your first revision, it wasn't quite clear to me what you meant.
I think that in order to see if this could/should be done we'd need to consider some things. First thing first, stats. How many users from those that post off topic questions do not have accounts in any SE site? Personally I've seen very few, but I'm not aware of the actual numbers.
Second, it's not necessarily true that a user with no account except MSO will ask only off topic questions. Say there is a new user that comes here, actually reads the FAQ and asks "What site could be appropriate for my question X?"
That doesn't look like a bad/off topic question to me and actually I think it's a normal question for Meta. I disagree that closing MSO to anyone who does not have an account is the best solution or even a solution at all to a problem which we don't know the size yet.