How can I create a Views RSS of members only content?
Yes. The forum/%forum_forum route created by the Forum module does a user_access() check for the access content permission; any subpath of this route (e.g. your RSS view, forum/%forum_forum/rss.xml) will be checked as well.

You can override this via a hook_menu_alter() implementation:

/**
 * Implements hook_menu_alter().
 */
function MYMODULE_menu_alter(&amp;$items) {
  $items['forum/%forum_forum']['access callback'] = 'MYMODULE_forum_override';
}

function MYMODULE_forum_override() {
  return preg_match('/^forum\/(\d+)\/rss.xml$/', request_path());
}