If you locate my most recent "Quick Answers" result, note it does have a result, but note that it took 104 seconds!
This is much more than the Ajax timeout, but clearly the query didn't stop. This suggests a denial of service attack is possible by requesting a number of very long lasting queries.
The [feature-request] is a better UI when Ajax times out.
The [bug] is the SQL query is not aborted.
(This was promoted from a comment I was going to add here.)