It's not good for the diff at all.. Very short distances at low speeds is all that "donut" spare is really intended for.. IF you don;t mind giving up a bit of trunk space, a full sized spare is darned nice.. If you have to travel any distance on your current spare, and it's at all possible, put the spare on the rear, and move one of the rear tires up front..
Right..So the front tires have to have the exact same circumference or can it be a little different?
I think overall diameter might be prudent to mention here. If both tires have the same rolling radius, it should not affect the drive-train at all. Granted, a death donut is not for autocrossing, but it shouldnt have an adverse effect on the differential if it has the same overall diameter. Perhaps the term 'tire size' should be clarified...
...BTW your Bieber avatar is awesome.-Malone