You can do several things:
- purchase a second new tire to match the new replacement. Then you will need to keep the new pair on the same axle for rotations/cross rotations for +40,000 more miles. I did this on my RDX. I ended up leaving the newer set on the front 2X as long to wear them down more to catch up the older set. Did this so I can replace all 4 when due.
- purchase one used tire on eBay matching the other 3 tires tread depth, convert the new tire into a full size spare. I purchased a used Conti DWS 06 tire on eBay at 75%-80% tread for about $80+shipping as a full size spare. Prefer a full size tire compared to a donut so I will have normal driving/braking performance.
The sh-awd system seems to be very reliable system. I don't remember any threads on two different Acura forums about having issues with sh-awd in the last 10 years. I've had/read issues with the sh-awd going into "limp mode"; but, that was to protect the system because something else was wrong with the vehicle (usually electrical related). I think the sh-awd system can handle short-term tread depth (circumference) differences like you have with a donut spare; but, I don't know how the system would react with +3yrs/+30,000 miles with different tread depth?
I would also think there might be a tire performance difference with one new and 3 old tires. Braking, acceleration, bad weather performance, or cornering seems to be effected as tires wears. The MDX might have to work a little harder to compensate for that?