Zenphoto uses the $_REQUEST super global to send the search queries. So http://www.zenphoto.org/page/search/?words=admin does work if called directly. But the standard search form uses POST instead of this GET example so there is generally no direct url to track.
You would have to create your own searchform. Look at the existing one and the class-search.php file. Also there is a search statistic plugin available in Zenphoto itself.
The modrewrite url to a tag is something like this `http://www.zenphoto.org/page/search/tags/admin`