No, I believe that every question-asker must make some attempt to apply Skepticism in the content of their question.
Otherwise this site is essentially a less social-networked [Quora][1]Quora and you can ask anything about any subject.
The problem is that the experts here are supposed to be focused on Skepticism, rather than a Jeopardy-like knowledge of everything.
If a question does not have a direct reference to skepticism or a claim they are skeptical of, then a comment should be left asking the asker to improve their question. If they do not, then downvote or vote-to-close. If they are a repeat offender, then you may even skip the comment part.
Of course, every user has a right to police the site how they see fit. [1]: http://www.quora.com/