Gibon2,
The high angle of attack protection mode does incorporate phugoid dampening. How effective it is at various altitudes and over the longer term is an open question.
Should you manage to disconnect the autothrust, idle the engines and then pull the stick fully back you will first be climbing as you trade your airspeed for altitude. As the speed decreases the α increases until it reaches α-prot at which point the angle of attack protection mode is activated. The flight control system is now locked in this mode and will maintain α-prot even if you release the stick, should you keep the stick fully back α will increase to α-max. It is worth noting that increasing α also increases drag which again will increase rate of descent. Do you know how to get out of the high angle of attack protection mode?
The only energy you- or rather the aircraft as you now have limited control of pitch- have available at this point to counter the drag is potential energy. The only way to use this energy is to lower the nose. The more drag the lower the nose has to be.
Just before you hit the ground you will also notice that you are unable to arrest the rate of descent as the stick is already pulled as far back as it will go.