Preowned/Used Games for PS4

As DGarvanski has already covered, there isn't any weird checking if you want to use pre-owned games on PS4. Like most pre-owned games however, if there was any additional content that was unlocked by the use of downloadable content, or passes or something similar, the likelihood of this still being available for a pre-owned game is unlikely, as they are only one-time use.

For future reference, Playstation have released an official guide for sharing/using pre-owned games on the Playstation 4 system:

Yes, you can play it normally. The PS4 allows the use of pre-owned games without any online checks or weird DRM. I've checked and Call of Duty: AW has no "Online Pass" system in place so you wouldn't have to buy anything extra in order to play. The only thing that will be different is if you buy a special edition since you wouldn't have access to the DLC that comes with that edition unless you buy it separately . However, the PS4 will not have any problems with you playing a used copy.