How to check if an URL is accessible by the anonymous user?

I need to find out if a given URL (specifically, the current URL) is accessible (ie returns HTTP 2xx/3xx) to a user (specifically, the anonymous user).
Thing is, the URLs are not always nodes, otherwise I might use the node_access API function. So at the moment I'm doing something like this, with curl:

function is_403(){
  global $base_url;
  $url = url($base_url.request_uri());

  $ch = curl_init($url);
  curl_setopt_array($ch, array(CURLOPT_RETURNTRANSFER => true, CURLOPT_NOBODY => true));

  if ((curl_exec($ch) != 0) 
  || (curl_getinfo($ch, CURLINFO_HTTP_CODE) == 403)) $denied = TRUE;

  curl_close($ch);
  return $denied;
}

So I'm using curl to let PHP make a request for me, for which I then read the HTTP status code. This works fine, but just doesn't seem right.
How could I do this from within Drupal, without making a separate HTTP request?