The carriers aren't sailing around alone - they're escorted by a whole fleet (plus air patrol) that will intercept the drone launching vehicle at multiple dozen nautical miles range. Smaller quadcopter drones won't even get close to catching the carrier (which can travel over 40 kts while evading) before their batteries die. And even if a few hundred got through, how much damage can they really do? I'd imagine the flight decks can be patched quickly, although some radar equipment & any jets parked at the time of the attack would probably be lost.
It's definitely a concern as part of a larger attack, but I don't think a quadcopter drone swarm alone is likely to sink a carrier or leave it combat ineffective in the long term.