here is a quick solution to get the post count any kind of filtering you want

    function custom_get_user_posts_count($user_id,$args );	
    	$args['author'] = $user;
    	$args['fields'] = 'ids';
    	$ps = get_posts($args);
    	return count($ps);
    }

since  this function uses get_posts you can filter and use anything that you can with [**`WP_Query`**][1]

so in your case you can use it like this:

    $count = custom_get_user_posts_count($user_id,array('post_type' =>'post','post_status'=> 'draft'));


  [1]: http://codex.wordpress.org/Class_Reference/WP_Query