It'd be better than so spare at all, but... your PCM may throw a fit.
I don't know what would trip, but there are anti-lock braking sensors to consider, of which traction control uses a portion of that system, Roll Stability Control (also uses much of the ABS hardware).
As for diffs, the front is a clutch-type limited slip (on all Super Duty Tremors), so you'd want at least one front hub in freewheel) and the rear diff is open until it is E-locked by the driver.
Other than that you'd have a bit of a traction problem w/ the smaller tire since the other three, larger-diameter tires would be taking the truck's weight away from the smaller tire's contact patch.
There may be more but that's all I can muster at the moment.
IMHO one should always buy five matching tires on five matching wheels because of the above factoids (then you have the option to run five-tire tire rotations! and have a 20 or 25% longer tire lifespan). I am compelled to have my exhaust system tailpipe section modified in order to carry my 37" spare tire and wheel in it's factory nest under the rear of the truck but right now it's taking up valuable space in my Tremor's bed.