You don't get a box; but if you ask for documentation, there is an insert they are giving out. AppleCare+ or AppleCare for that matter auto enrolls the device (Mac, iOS device) immediately when you purchase the device and AppleCare on the same receipt. That's a great benefit imo.
AppleCare/+ Does not cover lost or stolen iPhone's. That's what your cell phone insurance or home owners insurance covers.