Under the discipline of Human Computer Interaction (HCI) there have been numerous studies on the influence of the search User Interface (UI) on search behaviour. To my knowledge I am not aware of any empirical research that investigates the gathering of user feedback from the interface of an enterprise search UI. I performed some analysis recently on the impact of moving the user feedback option (button) in an enterprise search UI from the bottom to the top of the search results page. It appears to have a significant effect on how much user feedback is captured (see below).
Feedback (as a percentage of all search queries made) went from 0.2% to 0.8% an increase of 400%. True A/B testing was not applied as this was done sequentially not in parallel. However, from the feedback comments and quantitative log data, before and after the UI change there was no significant change in other enterprise search factors (e.g. indexing speed, failed searches, usage volumes). This indicates the UI change as the most likely reason for increased feedback.