You're probably going to wear on the traction lok more than normal, but if you absolutely have to then you have to. It's not recommended for long trips just long enough to get you to a tire shop and get a new tire on your rim.
You would have to drive for quite some time to damage the diff. The bigger question is will the donut clear the front calipers. I would try it and see before you end up stuck in the middle of nowhere with a spare that doesn't fit.
The mini spare will only fit the rear end and not clear the front Brembo brakes. I personally would care a mini spare so that I could avoid a tow truck disaster in towing to a tire store. If a front tire goes down, put the mini spare on the back and then place a rear tire on the front to get mobile again and out of trouble. Yes you have to change two tires but it beats heading to a body shop to fix the tow damage and pay for the tow job. Get a junk yard spare and jack set for peace of Mustang mind.