Restrictions and Limitations
Like AdSense for content, a publisher wanting to use AdSense for search (you can apply for either or both programs) must conform to the AdSense program policies. This means that sites displaying adult- or gambling-oriented content or encouraging illegal acts, among other things, cannot use AdSense for search.
A publisher cannot prepopulate the search box with suggested search terms: All input to the box must originate with the searcher.
Note that unlike AdSense for content, Google reserves the right to claw back some of a publisher's earnings from AdSense for search if Google's share of the ad revenue from those searches isn't enough to cover the cost of providing those searches. Google claims that fewer than one percent of publishers are affected by this clawback.
AdSense for search is not suitable for password-protected or very dynamic sites because only pages in Google's index are searchable. New pages won't be searchable until they are indexed, which may take a few days to occur.