Rather than not do any damage, the Escort Drone will essentially hunt you down and kill you. You’ll see the chopper blades spinning towards you like Jaws in the water, and it’ll eventually stalk you down and kill you.
It’s a bit frustrating, so we would highly recommend not using the Escort Drone until Treyarch has been able to issue a patch for it. Well, you could use it, but you might hurt your kill-to-death ratio a bit. No one wants that, right?