Since the basic WP Admin Category Search was downloaded more than a hundred times, I decided to make a PRO version of it.
You have all the basic things that are in the simple version, but the PRO version features an autocomplete functionality.
This autocomplete takes the suggestions from the categories and when you select a value, that gets checked automatically.
The other functionality stays, so if you write like 3 letters, you just push the GO button and it will filter the list.
Here is the PRO version: http://www.gadratilprogramming.net/shop/wordpress-plugins/wp-admin-category-search-pro/