In Normal law the aircraft will not provide a progressive pitch down. This is speed stabilities which are active in alternate law with protections only. It occurs between 5-10kts above the stall. In this case at alpha prot plus 1 the AP disconnects. At alpha floor toga is applied and as said before the aircraft will with a neutral side stick maintain alpha prot. To exit alpha prot the auto thrust must be disconnected and the angle of attack reduced.
That's the theory anyway and it works. However every aircraft and system has its limits and if the downdraft was strong enough insufficient lift would be the result in all cases.