That must be the only transmission on the ALHs 99-03? Why is the 01M a crappy tranny? Was it problematic and high maintenance?
Yes, and yes. The reasons are many.
I wouldn't buy a TDI with the 01M 4 speed automatic and so wouldn't even consider swapping it into anything else.
As oilhammer says, I will bolt up but there are several other issues to possibly resolve (other than the 01M being trouble) with making the Transmission Control Module happy since shift points and operation are electronically controlled.
The 09A 5 speed unit is much better, but again, getting the TCM to operate properly might be a gamble. Maybe get in contact with the guys that did the swap and find out if they ran into any such problems and if so, how they overcame them. Most of the time guys that have done stuff like that are willing to share the experience.
Perhaps some larger diameter wheels/tires combination might accomplish enough of a change?