I was wondering if any of the (E)GPWS callouts would make the autopilot disconnect? If the Alpha Protection is active (like in Bilbao, 2014) would it disconnect? That would give PF full control of the aircraft and could help to recover from the upset, correct?
This is the Quick Reference Handbook procedure from an old A320 training manual.
(The EGPWS procedure is a memory item, pilot's are not expected to look this page up when they encounter a EGPWS warning)
The first two sub items answer your questions. The autopilot needs to be switched off manually and the instruction is to
pull up to full back stick and maintain. The Alpha protection will prevent the aircraft from stalling, that is why the stick can be maintained at full back deflection.
Airbus' safety magazine FAST #23(PDF) giving guidance on flying protected aircraft, specifically advices pilots to apply full backward stick deflection in GPWS situations since the alpha protection will prevent the aircraft from stalling and the resulting flight path is the most effective way away from danger.
To illustrate a possible the effects of Alpha protection in an (E)GPWS situations, let's go to Bilbao again, but now in March 2001(PDF). An A320 on final approach encountered a wind shear causing the aircraft to descent fast. This caused the GPWS to trigger a warning. The pilot applied TOGA power and back stick deflection, but the Alpha protection predicted the aircraft to stall and prevented a higher nose attitude. As a result the aircraft didn't stall but crash landed on runway threshold. This accident demonstrates that the GPWS does not affect the flight envelope protection system.