What do you call a Q&A user who posts a question but never checks back?

This kind of user is called an ask-and-run.

It is even mentioned on Meta Stack Overflow: Dealing with “ask-and-run” questioners

Bonus: If we follow the same pattern, we can also come up with a specific term ask-and-idle for users who post a question but stay idle (but don't disappear/leave) without accepting an answer, commenting, replying to people, etc.

There is also the term Hit-and-run posting (thus hit-and-run poster) but it is a more general term and it is usually used for a one-off forum posting posted by a hit-and-run poster that ignites discussion. The motive of a hit-and-run posting is usually flamebaiting (posting a provocative or offensive message).

Hit-and-run posting refers to a tactic where a poster at an Internet forum enters, makes a post, only to disappear immediately after. The term comes from the hit-and-run crime on auto vehicles, in which the driver hits another car or person causing an accident and runs away. It is also known as making a "drive-by" posting, a play on the phrase drive-by shooting. The post often consists of a lengthy text making lots of claims that can be, but are not always, on topic.

http://en.wikipedia.org/wiki/Hit-and-run_posting

These users appear for a short time before disappearing forever, resembling the behaviors of virtual particles in quantum field theory, and therefore I would like to nickname them Q&A fluctuation: the temporary appearance of contribution out of empty space.

New answer (see below for the original)

Remorseful Querent or Regretful Querent

(the following analysis, especially the part involving “ridicule,” would also apply to “Remorseful/Regretful Respondents/Commentators” when they immediately regret having offered a response or comment):

According to Wikipedia, a Querent is "a person who questions an Oracle."

A “remorseful or regretful Querent” would describe someone who, immediate after asking the Oracle a question, regrets that he/she dared to ask it in the first place and therefore opts to leave the presence of the Oracle before getting an answer.
The regret or remorse could result from fear of one of two things, i.e., that the Oracle’s answer will be one, even THE one, that the Querent does not want to hear or that the Querent’s question will be ridiculed by the Oracle.

It’s not too ridiculous, at least to me, to view this forum as the Oracle and to view the forum’s “Users” as the Querents (granted, its Users can also be respondents and as such serve to comprise the Oracle).

Just as it would be naive to deny that most of the examples of “hit/ask/answer-and-run” questions/answers are probably posted by the “hit/ask/answer-and-run-type of “users” that merit our blame and condemnation, it would be equally naive to deny that the Oracle itself sometimes merits blame and condemnation when it inflicts hurtful ridicule on Querents (and respondents), to the very point of making them so genuinely regret having participated at all that they opt to escape the situation with their dignity (beyond the Oracle’s walls) intact.

(In my opinion, any claim that these “Regretful/Remorseful Querents/respondents/commenters” should have just; 1) never asked/responded/commented such “ridiculousness” in the first place; 2) immediately deleted their “ridiculous” questions/responses/comments (instead of just leaving them posted for further ridicule); or 3) “hung tough,” endured the well-deserved ridicule, and, as a drastic, last resort, acknowledged any injurious comments with a “flag,” is missing the whole point of “Regretful/Remorseful Querents/respondents/commenters,” and in doing so, stands as evidence that the concept exists and that it is a legitimate problem.)

(PS I wrote the above before seeing any of the last few comments under my original answer, and I now see that @Jon Story beat me to it and said so clearly and exactly what my babbling above is trying to say, but I'll go ahead and post it as originally babbled anyway.)

Original "Answer"

Such dangling or hanging queries are often asked by dis/uninterested inquisitors and sometimes by skeptical or reluctant querents.

They are, of course, known to their former teachers, relatives, and friends as "Easily Distracted".

"I don't remember asking any question"?