search does not yield access restricted results

If you setting the posts to private in WordPress, you can add this to your functions.php file:

function include_private_in_search( $query ) {
  // not an admin page and is the main query
  if (!is_admin() && $query->is_main_query()){
     $query->set( 'post_status', array ( 'publish', 'private' ) );
  }
}
add_action( 'pre_get_posts', 'include_private_in_search' );

Then you can format the search results page to show the excerpt and image.