I don't know the redundancy logic for the AH, but looking at the A-330 cockpit it looks like a separate instrument, even if it is a mini-screen instead of mechanical.
http://www.flickr.com/photos/jpavao/4644756009/
I would have also thought that the Pilots Handbook would give details on which instruments are powered by what for use in emergency situations.
I would also hope that the certification authorities would demand some sort of back-up for the triple redundant computer...:^)
It is my understanding that there is no backup to the triply-redundant FCS on the Airbus, other than a back-up software system, but that requires good air-data to work.
I know Boeing has looked at quad-redundant systems but I'm not sure what aircraft they use them on, if any. It is my understanding that Boeing does have a back-up system outside the FC computers, but I'm not sure of that.