Google generally places 3-4 ads (sometimes more depending on the search term) above organic results in the search engine. My experience in SEO and doing SEO has found that generally, the following statistics (approx) is true regarding the percentage of traffic to the site when ranked in the following positions:
1 - 56%
2 - 13.5%
3 - 9.8%
4 - 4%
5 - 4.8%
6 - 3.3%
7 - 0.4% (generally because of where this result is on people's screens)
8 - 3%
9 - 1.5%
10 - 2.6%
These figures are approximate and can change when looking at different and higher ranking terms. This is just a general overview of percentages of traffic from those queries to particular sites, from my experience.
As a result, the first 5 results take up ~88.1% of all traffic to that particular search term/query. FWIW when I'm doing SEO, I'm only interested in ranking in the first #3 results.
Hence, if you rank #1 in the search engine and there are ads above you, you aren't getting all of the traffic (which of course is why they are there so Google can make money). Hence adding Adwords ads to that particular query and search term, depending on your adwords quality score and if you can get it into the top #3 main ads then you are obviously going to increase your traffic to your website.
Why?
Well if you're #1 in organic results AND you have an adwords ad in the top 3-4 main spots then you have 2 positions in the top #5 results for the query which are receiving ~88.1% of the clicks by users - and having 2 spots in the most trafficed positions you're obviously going to see an increase in clicks!