Check if taxonomy is attached to at least one post in a post-type

It’s OK. The only problem I can see with this solution, is that you select all post data just to check if such post exists (and posts can be long).

So I would consider using custom query in this case (it gives you number of posts with this term assigned)

function my_count_posts_with_term($taxonomy, $term_slug, $post_type) {
    $term = get_term_by( 'slug', $term_slug, $taxonomy );

    $count = $wpdb->get_var($wpdb->prepare(
        "SELECT COUNT(*) FROM {$wpdb->posts}
        INNER JOIN {$wpdb->term_relationships}
            ON ({$wpdb->posts}.ID = {$wpdb->term_relationships}.object_id)
        INNER JOIN {$wpdb->term_taxonomy}
            ON ({$wpdb->term_relationships}.term_taxonomy_id = {$wpdb->term_taxonomy}.term_taxonomy_id)
        WHERE {$wpdb->posts}.post_type = %s
            AND {$wpdb->term_taxonomy}.taxonomy = %s
            AND {$wpdb->term_taxonomy}.term_id = %d;", $post_type, $taxonomy, $term->term_id));
    return $count;
}