Given that they ship animals and the contents of people's luggage would not survive freezing or a vacuum, I'm fairly sure it's more than adequate. Maybe not so much for the landing gear, which some people will also try to hitch a ride in (often fatally).
There is just conveniently space next to the box for him to get out of the box? Would think cargo holds are generally pretty stuffed full.
If it were strapped to a pallet or something, it would make its own space. It probably would be anyway becauee of the weight of the box.