Let me expalin. I noticed a new competitor company to mine. She was ranking really well with keywords I was competing for in the organic search and she had only been around a couple of months. The only thing I could tell she did differently than me was that she had an adword campaign. Does Google play favorites and give you a boost in organic listings if you are also playing in Adwords? Thoughts?
No, they don't. But it does allow other sites to notice your site, and other people will possibly link to your site. You'll also get more visitors and therefore more authority etc... But it does not directly increase your organic search results.
From my own experience, paying thousands for adwords did not help my natural rankings. And that's the way it should be. But it increased my traffic, which increased the value of my site when it came time to sell.
Adwords doesn't play roll to boost ranking in SERP because its completely paid. To boost ranking in SERP use ethical SEO technique for site like advertise your site through link building.
Not from a technical perspective, no,, Adwords does nothing "directly" to boost your SEO algorithmically. How ever, PPC will of course increase brand awareness, customer base and just general buzz around a brand and as miakiru pointed out, more people know about you, more people will talk about and link to you. It also enhances keyword reserch so she might be able to target more keywords more accurately.... and hence, boost overall SEO strength.
Could the opposite be true? i.e AdWords campaign running => So this is a commercial site => lets give it less natural search traffic?
I've said this before, but it's worth repeating,as the question keeps getting repeated. You can find as many people swear blind that adwords hindered their organic results as helped it. They can't both be right. They can both be wrong.
You talking SEO here right? I am guessing, if you buy Google's product, they are going to treat you good. Why wouldn't they?