Google adsense is irrelevant in the SERPs, it will not help or hurt you. Use if you want to, but don't feel like it is an obligation.
Is this a fact? Has Google said so? Well my personal experience is that there is some connection between SERPs & CPC. May be my CPC increase was due to something else which I did not notice. But I noticed higher CPC with Higher SERPs.
My experience is that it do affect the ranking. At the beginning I do not put adsense to a site. When I put it my rankings gets affected but not drastically, usually 1-5 spots.