You'd need to add a hook somehwere to record the info yourself (like adding a trigger to the "SurveyResults" table to replicate the same info plus a timestamp into your own custom table).  

If you're trying to figure it out for a survey that's already happened, I think your only bet is to try to get a general idea by matching USERID of the survey submissions with USERID visiting the survey page in the Site Log. This would hardly be considered a reliable method since a user could visit the survey page many times but only take the survey once (so you couldn't tell on which visit the survey was actually taken).  If a user who took the survey only visited the page one time, though, the Site Log would be pretty helpful.  That's all assuming that you have site log enabled...
 
Good luck!
-mamlin