Add Autocomplete to Search Block.

Could autocompletion be added to the Search Block as well.
I have used this to put a search in my navigation menu.

This could use the same permissions and settings as the theme search box.
Adding the following code in search_autocomplete_form_alter after the
search_theme_form code would acheive this.

    if ($form_id == "search_block_form") {
        $form["search_block_form_keys"]["#autocomplete_path"] = "search_autocomplete/autocomplete';
    }