Nope that’s not how it works. Why would you add it to the Menu if its private? If you click on the menu item it does not show the content correct?
http://codex.wordpress.org/Content_Visibility
You would add a private page to the menu to make it quickly available to Editors and Admins. It seems perfectly logical to add it to the menu, but only show the menu item when the user is authenticated and in one of the permitted roles. It seems like in WP I will have to take the extra step of emailing the URL of the private page to the Editors because they won’t find it in the menus.
I wrote a CMS in .net about 10 years ago, with users and roles. Pages automatically correspond to menu items, and the menu item appears based on the current user’s role, and in a different color (css based) to differentiate them from normal menu items. It is still in use on several sites, but I had to use WP for a new project.
Give this a look. You can make the menu conditional on User Roles.
http://themify.me/conditional-menus
