Just fished out the old manuals and dusted them off.
Nope the pressure setting is not an input to the CADC. Power, Pitot, static, TAT and weight on wheels are the only inputs.
It doesnt go into details apart from saying that it continually uses and analysis mathematical logarithms and formulae to compute everything else from these basic inputs.
P.F.M. I suppose (Pure Fecking Magic)
T.