I think the suggestion was more that you identify specific search urls which did not return a good result (hence the user went off to google). You could do this anonymously without tracking anyone or their usage of google or other search engines, or looking at the results on google.

As a DDG user I'd be really happy if you did this and think it would be the best way of identifying searches I'm unhappy with. I go to google now only if I'm not happy with the results from DDG.