Read post meta values, only if posts are public

Yes, do an INNER JOIN, something like this should work:

$values = $wpdb->get_col($wpdb->prepare("
    SELECT meta_value FROM $wpdb->postmeta
    INNER JOIN $wpdb->posts
      {$wpdb->posts}.ID = {$wpdb->postmeta}.post_id
    WHERE meta_key= %s 
    AND {$wpdb->posts}.post_status="publish""
,$metakey
));

I changed $wpdb->get_results() to $wpdb->get_col() since it looks like you are just selecting a single column of data as an array. I also added $wpdb->prepare() since that is generally best practice.