I say yes, because a questions and answer site is exactly the right format for these. The question goes up and stays up; maybe someone will answer it months later, and the answer is still likely to be useful to the asker. And there's no need for extended discussion, just the occasional comment asking if a certain detail triggers an extra memory.
There have been such questions on Gaming Stack Exchange, in the
identify-this-game tag. As far as I can see, it's working pretty well. The question of whether to allow them has been debated there; it's mostly Jeff against and the community in favor. Note that the site-wide policy is that it is up to individual sites to decide on the viability of identity-this questions.
For an example of a place where it works (as long as someone knows the answer now), if you manage to navigate through the spam, search for
yasid (yet another story id) on
rec.arts.sf.written and other newsgroups. Story identifications definitely bring good traffic there.
Just to insist: in 2010, people still came to a spam-ridden, politics-rant-infested newsgroup to have their YASID (yet another story identification) questions answered. Being good at story identification is definitely a benchmark at how attractive a discussion site about SF is. And story identification is ideally suited to a questions and answer format: one question, several possible answers, one of them correct.
If the questions offend you, put story-identification (or whatever we end up using) in your ignored tags list. And if the question is really terrible (“I read a book and it maybe had a green cover”, it can be closed, on merits, not because of its nature.