I already have search box on my blog

guessthelogo.net

This search box is nicely integrated with my blog template and I am not much interested in tampering the layout of the blog.

Can I make this search box to be used for Adsense for Search?

I am not sure whether Google Adsense allows this or not.

You can put a google search box on your site. You can use their search box for adsense as long as you don't violate their rule.