Many bloggers and site owners have Google Adsense for Search installed on their blogs. This ensures that you can provide relevant results to your blog users while simultaneously making some money on the side.
While, there is no issue with other users using the search box, however, the question arises on the legality of you using the same.
In a post on the Inside Adsense blog, Arlene Lee of Adsense Publisher Support has clarified that it is ok to search your own site with Adsense for search.
However, she strongly advises against using the same, simply because the probability of you clicking on your own ads increases tremendously, which will result in invalid clicks. You also increase the number of search query hits in the statistics.
If you would like to search your blog, then use the Google Toolbar, or even your inbuilt blog search.
You can use Google to search for your results in your site by using the site: keyword. e.g. to search within this site, I use site:techtites.com followed by the search query.