Not in a standard sense, i.e. the normal UI provided by Joomla. (Presuming you're talking about when an actual menu item is created here?) Extensions don't get a chance to run code when a menu item is created so, short answer: no.

I would normally suggest a plug-in but looking at `com_menu` I can only see two `JEventDispatcher` calls and they aren't very useful.

In `/administrator/components/com_menus/models/menutypes.php` you have:

	// Allow a system plugin to insert dynamic menu types to the list shown in menus:
	JEventDispatcher::getInstance()->trigger('onAfterGetMenuTypeOptions', array(&$list, $this));

And in `/administrator/components/com_menus/views/items/view.html.php` you have:

	// Allow a system plugin to insert dynamic menu types to the list shown in menus:
	JEventDispatcher::getInstance()->trigger('onBeforeRenderMenuItems', array($this));

Looking a layer deeper, the menu item class `MenusModelItem extends JModelAdmin` the good thing here is that `JModelAdmin` does trigger an `onContentChangeState()` event which you could trap and dis-allow anyone try to set your view to published if the user group is wrong.

Having said that, I wouldn't be doing that. Menu's are just paths and easy to guess in our SEO/SEF world. The right place to do it is in the component/view itself, rejecting anyone that isn't in the right group. You can do this either silently bouncing users back to the home page or throw a `404`.