Early March we reported that Google Tests Additional Sitewide Searchbox Within SERPs. Yes, for certain queries, Google will show a site search box, likely so they can increase search volume for the engine but say that they can help the searcher. In any event, since then I have been watching to find reports on what a search box like this would do to one's traffic.
One report via a WebmasterWorld thread reports that his traffic doubled due to the addition of the search box under his search listing in Google. Here are the exact words from the webmaster (see post #3592869):
They did one for my site. Works with a search for my domain. Traffic doubled overnight.
The thread is also analyzing how many pages a site has to have to be granted the site search box in the search results. There are sites found with less than 10,000 indexed pages with the site search box, according to the thread. But not everyone wants the site search box. Amazon.com for one doesn't. As you can see, when Google launched it, we took a screen capture of Amazon having the site search box, but now it is gone, because they asked Google to pull it.
If it increases traffic, then maybe it is worth keeping. Maybe Amazon thought that it would reduce traffic to their site, because the searcher would stay on Google one step longer and have less of a chance clicking over. Who knows?
I'll keep watching the space for signs of how this search box impacts webmasters.
Forum discussion at WebmasterWorld.