Can the Raven's Point Defense Drone counter 20 shots at once?

To answer the question in the title: no, it cannot. The cooldown is really short but isn't pure zero. That means that if there are a lot of simultaneous projectiles ("shots"), some of them can definitely reach their destination before the Point-Defense Drone will manage to intercept them.

Try the following experiment - put 4 Stalkers right next to a PDD and try to shoot it with all 4 simultaneously. Because the Stalkers are really close the PDD won't have time to intercept them all and the 4th Stalker will usually (not always!) manage to damage it, even though it still has a lot of energy.