I'm going to put a PHP domain name search function on my website. It will be one page among about thirty other pages and probably won't have anything on it that's likely to leap out for a search engine to put it ahead of all the other stuff on the website, none of which has anything to do with domain name searches. The odds are that the site will stay well below the early pages returned on any search. Probably a few thousand pages below them, which is fine with me because I'm not looking for high search engine ranking.

I see that a couple of scripts offer a randomly generated security code to prevent someone else linking their site to my searcher and blowing my bandwidth quota with their searches.

In my circumstances, is this a big risk that's worth having security protection against?

^

If you're concerned about it, you may want to check the referer for your search page against your site's domain and boot unidentified referers back to your homepage - additionally, you could include your search page in a robots.txt file to ensure it would not be spidered (and potentially confused as duplicate content) by search engines.