This is the question of a blogpost from the Google AdSense team.

"If you've added an AdSense for search box to your page, you're probably aware of the relevant search results it provides your users. That being said, a few publishers have asked us if it’s a violation of our program policies to perform searches in their own AdSense for search boxes."

http://adsense.blogspot.com/2008/09/is-it-right-to-search-on-your-own-site.html

"The short answer is no, this activity is not explicitly prohibited by our program policies."