In a word: yes.

I found a Firefox plugin that did that, and it worked, but it wasn't what I needed so I deleted it. Don't recall what it was called, but a quick Google look brought me back to it: here

It wasn't what I wanted because it only went to the search box when I loaded the Amazon site, rather than every time I wanted to do a new search while the site was already loaded.

tanstaafl.

Edit: Ooops... too late.