They do, but it's less helpful than it sounds. It only plays a sound if the AirPods are not in their case. Since I am fantastic at putting them in their case the instant they're not in my ears, I never have a chance to lose mine in a way where this feature would help.

Granted, it's harder to lose the entire case, though it's still small enough and made of slippery plastic that can slide out of pockets if you're unlucky.