Hi, I have no idea about Google Site Search. (http://www.google.com/sitesearch/) Please share with me if you have any experience on it. This tools will help to get better SERP result?
Sorry to disappoint but do not expect change in ranking because of this. It just searches through the indexed pages of your site in case you cannot build search for yourself which to search all pages, no matter if indexed or not...
Google has a support page, you can check it out, http://www.google.com/support/customsearch/bin/topic.py?topic=11503 Anyway, the tool is for you to search your website only, not the entire web.