in_category using array

I am trying to check if a title exists within a specific categories I want duplicate titles as long as they are in different categories. I think I need to use in_category with and array as the post_ID comparing if any of the post_ids are in the array. Thanks for any help.

global $wpdb;
if ($posts = $wpdb->get_results("SELECT ID FROM wp_posts WHERE post_title = '".mysql_real_escape_string($title)."' && post_status = 'publish'", 'ARRAY_A')) {
  if (in_category($cat, $posts) == 1) {
    //Do Nothing
  } else {
    //Do Something
  }
}