Upon close inspection of the live build videos, it looks like the AWD will be engaged at all times, but will indeed speed up the rear wheels whilst in drift mode (driven by the front axle through a couple of 12/20 gear pairs).
There are two driveshafts present, visible at several times during the first live build video (47:30, 2:31:15, and other timestamps). The main one is a direct drive between the two differentials. The alternate shaft is sped up via the two 12/20 gear pairs, once toward the front and again near the rear axle where the shift mechanism is. The shifter is a simple on/off: when off, the main driveshaft allows both differentials to rotate together and the reductions do nothing (the driving ring engages the 20 tooth gear on the second gear pair). When the clutch is engaged, the two gear pairs provide the path between front and rear diffs, and the main driveshaft idles. There is a slipper clutch of sorts (I don't recall what this is called, but it can be seen at 0:43 on the following video (lower right assembly on the thumbnail):
This will allow the main shaft to slip and prevent it from binding up the drivetrain when the car is in drift mode.
It's certainly not mechanically accurate compared to the real car, but I think it's a great solution that enhances its playability, and the effect is realistic in that a drifting car's drive wheels will spin faster than the others.
