Suppose I started a website where adsense publishers sign up to post data about what the AdSense for Search units they have published will be targeted toward. AdWords Advertisers can then use this information to create ads that adhere directly to the particular need. Theoretical example.. my small site about Tetris Attack clones doesn't carry the full array of links to different places you can go to play the clone called Cosmic Switch, so it informs the viewer that he or she must search elsewhere for "Cosmic Switch," and it would have my AdSense for Search unit adjacent to that. Then, I theoretically join said website so that AdWords advertisers can browse my directed keywords... and choose to design ad units aimed at those specific keywords. I'm wondering if this would be legal! If so, then... wouldn't it naturally benefit both publishers and advertisers?
So you are basically asking your users to use the search box ? I'm not sure if that's allowed. You're not allowed to ask them to click your ads ... so I would think the same goes for your search ...