No Rabbits came with AWD. Some of the later Golfs (A2 chassis) did and it was called Synchro. I think it was around 88 or later. But that was only in Europe. I dont believe they were ever officially imported into the US. So if you find one if was either imported or possibly brought down from Canada.

As for the question on converting one anythings possible. But you talking alot of money to find the parts and adapt them to a smaller chassis that was never meant for it. Plus you would need to do some serious engine mods. Those little motors they came with werent meant to push the extra weight and drive train loss of AWD.