To the contrary, SS ND inputs will get the airplane deeper into the high AoA protection
FCOM 1.27.20 P 4
To leave the angle-of-attack protection :
The sidestick must be pushed more than 8° forward, or
The sidestick must be pushed more than 0° forward, for at least 1 second, when α < α max, or
α < α prot, if the sidestick has not been deflected since the latest autopilot disconnection.