bear: I think you may be mixing normal law protections with alternate law stability functions.
In alternate law, the pitch
protections you mention do not fight as they aren't in operation. (Based on the much linked .pdf brief at smartcockpit, caveat, dated information). You do have high and low speed stability. Links here:
http://www.smartcockpit.com/data/pdf...light_Laws.pdf
and a link to a PPRuNe discussion on same from March 2009, pre AF 447 crash.
A320 Low speed stability [Archive] - PPRuNe Forums, is here.
Low and High Speed Stability: can make a nose down (if slow) or nose up(if fast) input in alternate law,
which the pilot can override. With double or triple ADR failure, you don't have either. (You are also paddling in a canoe up that proverbial creek ... ) But if you are in alternate law, it appears that you know you are required to fly by hand.
This goes back to the question raised a good while back: with airspeed signal being squirrely, did either
stability function (not protection) activate in an attempt to prevent either overspeed or stall?
Is that what you were getting at? Given that airspeed appears to be a trigger for one, and AoA and airspeed the trigger for the other ... good question. It appears that this is not an input that can override the pilots commands. (Toss in "Abnormal Attitude Law" and things get more interesting, I suppose ... if it's active)
Note of interest: from the much linked brief at smartcockpit ... dated info ... slide 5.24 ... page 64 ...
The ECAM system F/CTL page (Flight Controls?) has in the middle of the screen, just below center, Pitch Trim depicted numerically. I think that means THS trim angle, not sure. I will for the moment assume that to be the case.
If a flight control malfunction was not the highest priority ECAM alert (and how many of them were active?) then the PNF wold not be seeing that on the ECAM screen, and thus not have the info (were he looking there for indications of just what's amiss) he needed to cue the PF that
"THS is 13 deg nose up, move it/trim it down"
or words to that effect.