How AdSense Affects My Website's Search Rank

Users participating in Google AdSense will not see any effect on their website's search rankings compared to Web sites that aren't using AdSense.

Google won't either penalize nor reward your site for using AdSense.

Adding AdSense ads to your pages won't speed up crawling either. Your pages will be added to Googlebot queue as if they weren't using AdSense.

In other words, using AdSense on your pages doesn't have any impact on your search ranking nor speed your site is being indexed by Google.