I’m not sure I understand what you mean by category search field.
How difficult it is to search categories by a specific acf field depends on if you’re using ACF4 or ACF5.
In ACF 5 you can use get_terms() with a meta_query for the custom fields just like the meta query used for WP_Query().
In ACF 4 it is a lot more difficult. You’d need to get all the categories on your site and then loop through them and check the value the ACF field for each. If your time is worth anything then I’d suggest buying ACF5.