I'm almost positive it would light up with a spare. It probably has logic to compare both front wheels to each other, and both rears to each other, or something like that. That would make sense to me.
Of course it would be turning faster. The flattened bottom of the tire makes the effective ground-to-axle radius smaller. The top half doesn't matter, just the bottom.
Edit: in the case of the Corvette mentioned above, its front and rear tires are different sizes. (c6 has 25.7" dia fronts and 26.85" dia rears) There must be some compensation for that in the logic that controls the warning light.
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11-mile commute: 100 mpg - - - Tank: 90.2 mpg / 1191 miles
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