I am in the A330 fleet, the situation discussed here should be similar.
If an overspeed protection happening, no mater it is a true or false one, the protection function will trip off the AP and pull the aircraft up in 1.75 g for recovery and the pitch up command cannot be overriden by pilot's pitch down input. Until the disagree situation happens between ADR(s) and AOA(stall?), then automatic alternate law reversion happens and pilot's pitch down control can be achieved.
The question is if the aircraft went into deep stall before alternate law achieved, the recovery of the undesired aircraft attitude for the pilot could be a disaster. Refer to Airbus FCTM on Unreliable speed part, it mentions for extream case like we discuss here, switch off two ADRs will force the aircraft getting into alternate law right away, this may help to recover the unwanted overspeed and/or deep stall situation better.