AWD vehicles have 3 differentials - front, rear, and center. The job of the differential is to allow for a different speed between the front and rear axles (center diff), or between left and right sides (front and rear diffs).
This
video contains a great explanation of how a differential works.
The ring, pinion, and spider gears in a differential can handle a million miles of different rotational speeds.
An "open" (or unlimited slip) differential, will transfer all rotational energy to the wheel with the
least amount of traction. I.e., if your left tire is on pavement and your right tire is on ice, the left tire will remain stationary while the right tire spins uselessly. To combat this problem, your vehicle may have "limited slip" technology. This limits the amount of slip, or speed difference. This technology can be implemented either by a set of gears (Torsen style) or by a set of friction clutches. This
video explains how a clutch pack limited slip works.
Theoretically, if you have 2 different sized tires, you will have constant difference in wheel rotational speed, but not enough difference to lock the output shafts together, and thus create premature wear of the clutch friction discs.
If you run the math on tire size, you'll find there's an approximately 2.5% difference between brand new and fully worn tires.
Is that enough to cause premature wear? If so, how long before this becomes an issue? It's not really clear.
You should weigh your ability to purchase 2 vs. 1 tires against possible repairs later in the vehicles life (much greater than 100k miles would be my guess).
