If you buy a used air conditioning control unit it will probably work without any need of coding, maybe only a few minor changes if the unit was originally installed in a cabrio or a RHD/LHD setting different from your car.
But I think there's something you should consider before starting such retrofit. After finishing the retrofit in my car I discovered an additional issue that may be the most relevant: fresh air/recirculation works differently in the automatic and manual air conditioning boxes. The recirculation flap motor has a potentiometer to control its position in the automatic version, while there is no potentiometer in the manual version. The auto control unit signals an error when it detects that the potentiometer is not present and it seems to stop sending signals to the motor, or sends the signals intermittently.
I tried to solve this by replacing my original motor with another with the potentiometer, but doing that alone didn't solve the problem. Actually, I discovered that the whole reciculation flap assembly is different in the two versions. While in the manual version the motor moves only about 1/4 of a turn, moving from full recirculation at ont end to full fresh air at the other, in the auto version it rotates about 3/4 of a turn, beginning with full recirculation, passing slowly through partial recirculation/fresh air up to full fresh air, then it quickly returns to full recirculation. While the manual recirculation box movement range is a short "closed-to-open", the auto version range is much wider "closed-to-open-to-closed". Simply replacing the motor causes the control unit to signal an "actuator stuck" DTC because the motor won't respond with the range of movement expected.
Replacing the recirculation flap assembly seems to be possible (and I even got the right part number for that) but according to Audi maintenance manuals it would require removing the whole air conditioning box, which would require removing the dash, which requires removing almost everything, so instead I decided to work on a simple analog circuit to convert the signals from the motor potentiometer to the range of values expected by the control unit. The one I currently have seems to work reasonably well, but I'm still improving it.