Here's a concept for the search box that makes it accessible all over the site, and still not that intrusive. Basically there's a small fixed row at the bottom of the page that's always there (a slightly darker color than the current page, so it looks recessed) and it's the component index. Clicking it would make it expand, taking over almost all of the screen (up to the top navigation, which will always remain visible).

Here's a concept for the search box that makes it accessible all over the site, and still not that intrusive. Basically there's a small fixed row at the bottom of the page that's always there (a slightly darker color than the current page, so it looks recessed) and it's the component index. Clicking it would make it expand, taking over almost all of the screen (up to the top navigation, which will always remain visible).