Sounds strange. You're saying one of the three ADC's have failed (there are some 744's with only two fitted)?
It could be airline specific. There are pin-programmed options regarding the number/type of sensors which must be available for engagement. There are also different engagement rules, depending on whether the aircraft is in the air or on the ground (the latter for maintenance purposes, of course).
However, if you have two functioning ADC's, I would have assumed two A/P's.
Do you have the exact wording of your QRH? Some ADC faults are generated by AOA sensor failures. There are only two AOA's, so this may be the reason you might only have one A/P available(?)
Regards.
NSEU