In an Airbus, if the AOA sensor fails and the computer pitches the plane down, can the computer still only pitch down 10 degrees maximum?
The answer below is for the A320, as this is the only Airbus manual I have access to.


  would it go into a ballistic, unrestricted and dangerously steep dive


It'd likely stop somewhere before that. "Abnormal attitude law" engages when:


Bank angle above 125°
Pitch above 50° nose up or below 30° nose down
KIAS below 60 to 90, or above 440
Mach above 0.91
AoA above 30° to 40°, or below -10°


I believe the FAC will also give up at some point as the computed KIAS is so far away from what is measured. If it is a double ADR failure or double FAC failure it will go down to Alternate Law. If it is a triple failure it would go to Direct Law, as was the case of GXL888T.