Is it possible to index custom page content?
Yes of course you can. You can use the hook_node_update_index() for this:

function YOURMODULE_node_update_index($node) {
   // here is an example that fetches content from an url and appends it to
   // to the data that will be indexed
   $ch = curl_init();
   curl_setopt($ch, CURLOPT_RETURNTRANSFER, TRUE);
   curl_setopt($ch, CURL_URL, "http://example.com/readme.txt");
   $content = curl_exec($ch);
   curl_close($ch);

   // return the extra content that needs to be indexed for this node
   return $content;
}


The above will of course only work if your custom pages are stored as nodes in Drupal. For instance if you have a node that is called contact which shows content generated externally, then you need to fetch the same content in hook_node_update_index() for this specific node.