I use the search box too, I only got 3 or 4 search per day, everyday and those search gives me nothing..but its' nice to have too, i guess...
Sorry for the delay on replying to this post. I don't know I have no tracking on the search box. You can however see what the user is searching for. Oddly it's normally not related to any pages on my website at all.
I made money too with the search box, but its wierd. People are wierd. They come to my site from Google and then leave my site using the Google search box. haha
Putting a search box on a information site is surely a gold mine. People will want to search around a bit
Your site must have at least 100 pages, so users to be forced to use the search instead of digging. Other option would be to use bad and non-intuitive navigation, which is very bad!
This to share with all of you guys that Google Search makes wonder for sure. One of my client from Canada is making $1000 per month only from google search BOX he has around 3.5k visitor per day on his website.