Manual says not to put the spare on the front. If you have a flat front tire, you must first swap the compact spare with a good tire on the rear. Then swap the flat with the good tire you removed from the rear.
That's assuming that you have stock size tires.
Having the doughnut on the rear in this situation, is going to put undue wear on the clutch packs in the LSD...
Bottom line, even "limping it home" on the doughnut is gonna put the hurt on something...