No......
The Red Top 4x4 engine used the Red Label WD048 where the system basically operates as the Red Top 2wd engine albeit with the ECU differences of the L8, but the Green Label WD048 used the Closed loop addition within the Ecu and the addition of the Lambda on the exhaust.
So to be clear, Green label Ecu will run closed loop in conjunction with the Lambda (and has previously unanswered possibly the loom too), whereas the Red Label WD048 runs without as standard as the Lambda in not enabled.
Stu@Msd can add the additional Mod to make the Red Label Ecu run closed loop if you are stuck with a red Label ecu.
Hope that helps.