Removing Uncategorized on post save if other category present?

Yes. You can use the save_post action and do it here is some function that remove the default wordpress category if there is some other category selected.

I added some comments so you will understand the process.

function remove_uncategorized($post_id) {
    // get default category
    $default_category = (int)get_option('default_category');
    // check if the post is in the default category
    if(in_category($default_category, $post_id)) {
        // get list of all the post categories
        $post_categories = get_the_category($post_id);

         // count the total of the categories
        $total_categories = count($post_categories);

        // check if the post is in more than 1 category (the default one and more..)
        if($total_categories > 1) {
            // remove the default category from the post
            wp_remove_object_terms($post_id, $default_category, 'category');
        }
    }
}
add_action( 'save_post', 'remove_uncategorized' );