Is there a way to disallow the node/* path for anonymous users?
You can give permission to particular node using hook_permission(). 

function your_module_name_permission() {
  return array(
    'access your modulename module' =&gt; array(
      'title' =&gt; t('Access your modulename module'),
      'description' =&gt; t('Allows access to your modulename module'),
      'restrict access' =&gt; TRUE
    ),
  );
}


and then go to permission section under people menu. and uncheck above created permission for anonymous user.