Yes, you can make a gt into an AWD. Its not to difficult if you have the know how and the right friends to help you. Its been done before and there is a well informed right up about how to to do it on www.3si.org
You can also drop in a TT into the fwd set up, or you can drop in a TT engine and tranny combo. The second option is a bit more tricky with cleaning up some of the unused chit, and having to weld the diff to keep from burning up the tranny if you are to remain FWD. Its not recommended to simply cap the rear output shaft of the tranny. The spider gears need to be welded, or so i've been told.
All in all nothing to difficult to do seeing how there are plenty of right ups about all the options you can think of. Chances are someone has done it already and left a link to a tutorial on how they did it. Just make sure you get some helpful people lined before hand cause if you eff up something a shop will rape you to fix it. Oh, and i wouldn't start counting on fellow owners to come through for ya either. I learned the hard way that most are out for themselves and don't know shit about the car anyway.

Good luck mang.