Kind of actually. If you set that PS4 as your main PS4 any software purchases will be tied to that box as well as your PSN account. I don't think he can download it again if he formats the box later, but that PS4 would be allowed to play the current COD installation without your user signed in.
Along the same lines. Make sure you deactivate a PS4 as your primary PS4 before selling or trading. You can only do it on the system and can't change to a new one without the other system deactivated. I don't know how this works for people who have their units replaced.