you can add a maximum of two Google AdSense for search boxes may be placed per page. Also, a single link unit or image ad only may be placed on pages with AdSense for search results. Queries must originate from users inputting data directly into the search box and cannot be modified. This includes pre-populating the search box with terms or hard-coding direct links to search results pages. AdSense for search code may not be integrated into any software application such as a toolbar
Google will ban you for that, if they find out. But do you really want to get a nerve breakdown every time the payment is delayed? It's against their rules. Also, against their rules is placing ads somewhere where people may accidentally click on them. So yeah, I wouldn't advise you to do that. I'm an AdSense user for a long time, however, I'm a Youtube publisher, so I don't know much about that. But I read something on the forum, and it's definitely against the rules, since it's endangering their marketing companies.
Google Adsense has load of rules and one wrong move, they will just go ahead and banned you. They won't even answer your email about it, and they don't much care if it is your fault or someone wronged you!
Yep, Google is like that. It can ban you without telling you a reason why, or letting you appeal that. When your Adsense account gets banned, that's it. There's nothing you can do about it. There's nobody you can contact about it, and nobody is going to help you with it, because those are the rules. If you do anything that may harm your account, you will always have a risk of getting banned without a word. Once you do get banned, if you do, God forbid, all the money you have earned is lost. Best not to screw around, folks.