I knew you would back out!
We can stop the guesswork, as I have a diagram too from the AMM:
The bellows do indeed have sense ports direct from the cabin. But as clearly visible it all takes place prior to the mix manifold. Hence, it is all exactly as I have been saying. The pack doesn't care what is going on in the mix manifold (I.e. If the recirculation fans are on or off).
The pack will deliver their fixed flow (biased for cabin altitude) and the outflow valve will adjust to maintain pressure accordingly.
The only responsibility of the recirculation fans is to... wait for it...
recirculate the air in the cabin.