Simple answer: no, Google doesn't give your 'organic' (natural) listings a nudge just because you're spending money with them.
The better answer though is that if you're spending money on Adwords, it should be a prerequisite that you look long and hard at your site content (especially for content relating to those keywords) before you run a campaign. In doing so, that optimisation will in itself help your site's performance in Google irrespective of your Adwords.
Put simply, it would be inconceivable that anyone would run an Adwords campaign without first looking critically at your site for the keywords you're about to buy. Why? Well, if you think those keywords are important enough to buy, your site must be strong on those keywords!