I've just been trying to read through FCOM 1 Flight controls reversion section. After i took a headache pill I found that following any ADR disagree reversion to ALT LAW the protections lost are:-
1/ Load Factor
2/ Pitch Att
3/ High AoA
4/ High Speed
5/ Bank Angle
And 6/ Low Energy
So to me it appears that the aircraft would not have "pitched up" automatically during what it thought was an overspeed situation.
It was basically left to the Pilots to correct any perceived overspeed/underspeed.