I do believe that Google AdWords (Paid Listing) and their Organic Rankings ('Free' Listing) are treated as 2 separate platforms. Therefore, they do not have any direct impact on one and other.
I have no personal research on the matter, or any statistics to hand, but this official Google AdWords Resource does back up my thoughts a little. More specifically, the quote:
Search listings are free, and no one can pay for a better ranking (Google AdWords)
Going by the above quote, your Google AdWords's activities should have no bearings on your SEO/SERP efforts.
Another key quote, being:
Google is committed to keeping our search content useful and trustworthy. (Google AdWords)
As you are likely aware, it takes a lot of effort and time to rank well for most search queries. Certainly, those with a commercial intent anyway.
To name a few reasons why:
- Content: Search Rankings factor in the quality, length and popularity of your content as well as the regularity of your publication(s);
- Back links: Links are also considered. It is said that each back link is seen as a 'vote of confidence' in a publication. The more 'votes', the better a piece of content is; generally. Of course, each vote being weighted slightly differently;
- Site Performance: Factors such as page load speed, site structure and overall user experience is considered too. It is assumed that a website, serious about producing great content, would also ensure that their website is 'technically sound' too;
- Engagement Levels: Similarly to the above, search rankings look at metrics, such as Bounce Rate, time spent on a site/page and the actual Click Through Rates (CTR) in the search rankings, as a means to establish whether a piece of content matches a user's search query and intent.
Of course, there are many more factors and metrics involved. The point being, all considered metrics, all serve one clear purpose:
To ensure that only trustworthy content rises to the top of the SERPs and to ensure that a user, lands on the most relevant content possible. (Myself)
In other words, satisfying Google's quote, about trustworthiness, above.
After all, Google wants its users to find its 'gigantic Library' useful. If a user does not, they will simply leave and find another source for information.
If Google were to allow their organic listings to be influenced by money, then it would completely undermine their whole system. It would eventually become an elitists race to the top. In other words ... Google's organic listing, would end up being dominated by whoever could pay the most and not whoever is able to provide the best possible content, for a user's search query.