I suppose the proper answer for this is "sort of." While the entire query isn't itself saved, SmarterTrack does offer a report on "KB Searches Without Results" that breaks down queries into individual words, shows the number of searches for that word and the average number of results returned. There's also a report on "KB Searches Without Views" that does something similar, showing searches customers have performed but, for whatever reason, didn't show relevant results.
Using these reports, you can find keywords that users are searching for and then manage your articles accordingly; either creating new articles or adjusting your keyword density within existing articles to show more or better results.
I hope that helps.