Attaching an Authenticator would be highly recommended, especially since you have a World of Warcraft license, other games aren’t as big a target because they don’t have tradable currencies, though still recommended.
I don’t know how much visibility we’d have into Call of Duty activity other than how you logged into the game through Battle.net. While it is a game that is launched through our platform, it isn’t run by Blizzard, it’s an Activision game. Outside of purchase and installation issues, you’d want to reach out to their support with any issues you may have with access.