I know the mk3 2.2 has a 6 speed box, not sure on the 2.0.
The bit that gets me wondering is the can of worms you may open with the ecu, if you keep the old 2.0 one then it will almost certainly need some reprogramming. I don't know if you can just swop it out with the 2.2 without upsetting the immobiliser and so on.