I dont know much but I think there is some connection as I have had some improvement in my SERPs after an adwords campaign ...
Alex depends on what you are looking for, AdWords is a great tool for market research, advertising and also branding Running and effective campaign may increase your brands awareness (esp bidding for top positions) and this in turn could over time encourage people to search for you and not your product
It can work if you encourage people to bookmark your site, add you to facebook, tweet about your site etc. Also people adding comments to your page if you have the facility will help with freshness and could help with relevency.