I'm not sure how hard it would be to create a reliable test for clicks. Depends on the type of click, I suppose. Some would be fairly easy to detect (e.g., "for .1s, all samples output are 0, with loud samples on both sides"). Though I'm guessing that would actually result in plenty of false-positives, and would be a fairly carefully tuned (and thus fragile) test case.
A better approach might be to detect it in the frequency domain, after performing an FFT (that instant drop to 0 will generate a lot of energy on both sides). I suspect you'll still need the careful tuning; after all, a sudden burst of energy on your FFT could be a click, or it could be a cymbal.
Not sure how well this would work, I've never tried it, though it sounds like some fun code to write.
BUT, when QA team found problem, you can create automated test case, which will look for that particular problem only. Right?
For example, QA noticed "clicks" every few seconds in resulting sound. Is it hard to create automated test case for that?