no not the dumbest question, No audi is permanently 4 wheel drive even the a4,a6,a8 quattro, they are all two wheel drive untill differential passes power onto the rear of the car at a speed of approx 10kmph hence why the mot is never a problem on the rolling road.
the origional TT only came out in quattro at first then introduced the two wheel drive model a couple of years later. however due to the set up of the haldex quattro system the car is only ever in 4 wheel drive mode when required and is activated by the the haldex ecu.
instances when the tt will engage 4 wheel drive are on full acceleration on sharp turning, or possible when spinning on its axis, which is recognised but the yaw rate, longitudinal and lateral acceleration sensors.
The bottom line answer is, if we just say audi quattro is considered 4wd by majority of all non technical people, then no the MK1 TT was not solely 4WD, they did a 4WD & a FWD, simple answer to simple question.
But Foolish is obviously correct its not a permanent full on 4wd system, it works when it needs to.