Enter the MAC of the Box and press the Find button on this page:
If you see an error "404 Not Found", or if the date shown is more than 12 hours ago, then the Box has no Internet connection.
As background, even before a Box has been registered, it contacts the servers regularly to check for new firmware upgrades. So this tool works for both registered and unregistered Boxes. Also, Box checks for firmware upgrades within 1 minute of being powered-up, so this tool is reliable for determining whether the Box has a connection to the Internet.