No, it does not directly help with organic rankings, but one can argue that it does help with potential backlinks(in the scenario, however unlikely, that someone finds your ad, clicks on it, likes your website and decides to link to it). Re: Alexa, yeah sure it could effect your ranking/visitors if you were to spend a bunch of $$$ on adwords, but it would only be short term if you were to stop. As a long time internet marketer, I wouldnt really worry about your alexa rankings. Its not very accurate(its using its own datapoints-ie from its toolbar), and represents a small subsection of overall web traffic. Compete/Quantcast/Hitwise are usually more reliable, but all of them a trumped by your own analytics data(wether it be Google Analytics or an enterprise tool like Ominture)
Some text based ads do help with backlinks. However, adwords do not. Google has omitted them from the Algorithm
Adwords DOES NOT help SEo (apart from the extremely unlikely indirect method explained by Fletch_123)
There is no PPC programme I know of that will help your SEO. Even if one was dofollow then you can bet that Google would devalue the links entirely