re: So could an aircraft carrier battle group fend off a large swarm of drones?

Yeah, but a drone can be a lot of things. And thousands of quad copters could do a lot of damage and be very difficult to shoot down. And that's only one kind of flying drone. All those above-the-surface weapons systems wouldn't be much use against a swarm of drones that just floated up, attached to the hull and exploded, making hundreds of holes throughout the length of all the ships in the battlegroup. Not that drone mines couldn't be defeated, but there's more than one way to sink a ship.