Check if post of title already exists

Yes $wpdb is built in and is loaded by the WordPress Core on every page load.

I don’t see any critical problem with your code. I am going to suggest some improvements because I see some places where could go wrong, but mostly that should work. That makes me think that $article->heading is not matching up to the inserted post_title. So…

Try to normalize your title with sanitize_title_with_dashes which is how WordPress builds the post slug, and then check for that slug instead.

global $wpdb;
        $query = $wpdb->prepare('SELECT ID FROM ' . $wpdb->posts . ' WHERE post_name = %s', sanitize_title_with_dashes($article->heading));
        $cID = $wpdb->get_var( $query );

Now your query is looking for post_name, which is the slug or permalink tail, and I changed $wpdb->query to $wpdb->get_var since you are looking for a single variable, which we save to $cID.

Use a better check for your conditional.

if ( !empty($cID) ) {

However, this might not be the right approach at all. Look into the XML_RPC API mentioned by @kaiser. It has post insertion capabilities.