Importance:
AWA
AWA explains that searches and AdWords do not affect one another.
AdWordsAdvisor Says: [
Link to quote]
Just wanted to jump in here with a brief observation.
In actual fact, things are simpler than implied above. Simply stated, the unpaid search and the paid advertising are 100% separate - and one does not effect the other in any way.
To put it another way, those in AdWords will not know if an advertiser appears in search or not. Likewise, those on the search team will not know if a site which appears in search is also advertised in AdWords.