Add a custom post when inserting a new user in WordPress?

I think you are making this a lot harder than it has to be.

1. Run your code on user_register and update_profile
2. Check to see if the post exists, and create it if not
3. Done. WordPress should take care of the rest.

Something like:

function register_user_pupil($user_id) {
  $current_user = new WP_User($user_id);

  $post_args = array(
    'post_title'      => $current_user->data->display_name,
    'post_type'       => 'pupil',
    'post_status'     => 'draft',             //This registration cpt is not available for public
    'post_author'     => $current_user->ID
  );
  $exists = new WP_Query($args);

  if (!$exists->have_posts()) {
    $postid_pupil = wp_insert_post( $post_args );
  }  

  //postid should return something above 0 and not a WP_Error-object
  if (is_array($postid_pupil) || intval($postid_pupil) === 0) {                        
      throw new Exception('Kan inte skapa en elev-registrering');
  }

  //Rest of updating is done by function postsubmit() (saving the pupil CPT)

}
add_action( 'profile_update', 'register_user_pupil');
add_action( 'user_register', 'register_user_pupil');

I don’t have your CPT and supporting code so I can’t really test that but I am pretty sure it is close.

WordPress will enforce unique email addresses so I don’t see the point of worrying about that.