Check If posts exist in custom post type category, outside of loop

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It all boils down to WP_Query in the end even if you use get_posts, here’s my modified version:

$hasposts = get_posts('post_type=sc-events&category=40');
if( !empty ( $hasposts ) ) {
    ..// show the drop down menu
}

or

$query = new WP_Query(array(
    'post_type' => 'sc-events',
    'category' => 40
));
if( $query->have_posts() ){
    echo 'we have posts';
} else {
    echo 'no posts found';
}

While this will work, there’s an alternative inspired by your own answer that uses the category slug rather than its ID:

$term = get_term_by('name', 'whatever category 40 is called', 'category');
if($term != false ){
    if($term->count > 0 ){
        // we have posts
    }
}