Hi 411A,
In this case, a 'no dual' message appears, and the approach is continued to category two minima.
I think that's an FAA regulation which didn't recognise the "double dual" redundancy in the Autopilot A/L system. The UK CAA permitted us to revert to CAT III single limits of 50 radio & 200m RVR with a "DANA" warning. PFM.
Interestingly - in the early days - it was only the UK which permitted us to use CAT IIIB NO DH, 75 m RVR limits. France etc. insisted we use CAT IIIB with 15 ft DH limit & 75m RVR (required a runway centre line light or marking to be visible). I believe this "mini DH" is coming back in again for low vis ops in France.