From the TireRack website:
Four-wheel drive and all-wheel drive vehicles are equipped with additional differentials and/or viscous couplings that are designed to allow momentary differences in wheel speeds when the vehicle turns a corner or temporarily spins a tire. However, if the differentials or viscous couplings are forced to operate 100% of the time because of mismatched tires, they will experience excessive heat and unwarranted wear until they fail.
This necessitates that four-wheel drive and all-wheel drive vehicles use tires that are very closely matched. This is because different diameter tires roll a different number of times each mile as a result of the variations in their circumferences. Tire diameter variations can be caused by accidentally using different sized tires, tires with different tread designs, tires made by different manufacturers, different inflation pressures or even tires worn to different tread depths.
As an example of different tire diameters resulting from tires worn to different tread depths, we'll compare two 225/45R17-sized tires, a new tire with its original tread depth of 10/32-inch and a second tire worn to 8/32-inch of remaining tread depth. The new 225/45R17-sized tire has a calculated diameter of 24.97", a circumference of 78.44" and will roll 835 times each mile. The same tire worn to 8/32-inch of remaining tread depth is calculated to be 1/8" shorter with a diameter of 24.84", have a circumference of 78.04" and will roll 839 times per mile. While the difference of 1/8" in overall diameter doesn't seem excessive, the resulting 4 revolutions per mile difference can place a continuous strain on the tires and vehicle's driveline. Obviously, the greater the difference in the tires' circumferences, the greater the resulting strain.
This makes maintaining the vehicle manufacturer's recommended tire inflation pressures and using "matched" tires on all wheel positions necessary procedures to reduce strain on the vehicle's driveline. Using "matched" tires means all four tires are the same brand, design and tread depth. Mixing tire brands, tread designs and tread depths may cause components in the vehicle's driveline to fail.
If it were up to me, I'd not risk the expensive repair later to save money now.