A Google user posts on the Google Groups asking whether signing up to a Google AdWords campaign will expedite her site listing in the organic SERPs.
However, AdWordsPro of Google writes to say that there is no correlation between PPC and organic listings:
It is very important to note that there is absolutely no connection between being an AdWords advertiser, and having your site appear in the unpaid search results. One does not effect the other in any way. To put it another way, being an AdWords advertisers will neither help nor harm your chances of appearing on the 'organic' search engine.
AdWordsPro adds that this information has been gathered after careful observation after "quite a few years at Google."
Still, this has been a "conspiracy theory," to quote Barry, since the inception of AdWords. From a Search Engine Watch Forums thread, a member noticed that his paused AdWords campaign yielded a drop in organic referrals as well. Member scrubs adds that "Over the last year I would say the AdWords algo is as complex and as clever as the natural algo. Both are looking at different aspects on page to warrent your position in the listings."