I agree with
Rainboe and others (above) in that I don't believe Dutch Roll is a factor in either the Classic or 744 airframes. I have flown the Classic with one Yaw Damper u/s on more than one occasion and experienced no adverse handling characteristics whatever. I have to hand an elderly copy of the the DDM for the Classic and it says that one Yaw Damper may be inoperative without restriction and adds ...
NOTE: Although flight control without Yaw Dampers is satisfactory, the structural substantiation of the aircraft requires one to be serviceable.
Furthermore, it lists Yaw Dampers under Automatic Flight (22) rather than under Flight Controls (27), which reinforces the supposition that Yaw Dampers are there on the 747 more to balance normal turning flight than to counter any Dutch Roll tendency, as in the VC10.
With this in mind, and with regard to the original question, I would suggest that the feedback loop in the yaw damper demand circuit would simply apply sufficient yaw to keep the aircraft in balance, irrespective of the the number of rudder surfaces actually being deflected. Therefore, in single Yaw Damper operation, the aircraft would still remain in balance by virtue of this feedback signal to the remaining Yaw Damper and not because of any wiffle-tree or other similar mechanical arrangement (as in the VC10 Feel System).
HTH
JD
