Probably not, as long as it is not smaller than the spare that normally accompanies the car, as long as you remember that AWD will likely be disabled, and as long as you don't drive over the recommended speed while on a spare tire per the OM.
For example, this is an excerpt from the 2013 SHO OM:
A dissimilar spare tire and wheel assembly is defined as a spare tire or
wheel that is different in brand, size or appearance from the road tires
and wheels and can be one of three types:
1. T-type mini-spare: This spare tire begins with the letter T for tire
size and may have Temporary Use Only molded in the sidewall.
2. Full-size dissimilar spare with label on wheel: This spare tire has
a label on the wheel that states: THIS TIRE AND WHEEL FOR
TEMPORARY USE ONLY
When driving with one of the dissimilar spare tires listed above, do not:
• exceed 50 mph (80 km/h).
• load the vehicle beyond maximum vehicle load rating listed on the Safety Compliance Label.
• tow a trailer.
• use snow chains on the end of the vehicle with the dissimilar spare tire.
• use more than one dissimilar spare tire at a time.
• use commercial car washing equipment.
• try to repair the dissimilar spare tire.
Use of one of the dissimilar spare tires listed above at any one wheel location can lead to impairment of the following:
• Handling, stability and braking performance
• Comfort and noise
• Ground clearance and parking at curbs
• Winter weather driving capability
• Wet weather driving capability
• All-wheel driving capability
3. Full-size dissimilar spare without label on wheel
When driving with the full-size dissimilar spare tire and wheel assembly, do not:
• exceed 70 mph (113 km/h).
• use more than one dissimilar spare tire and wheel at a time.
• use commercial car washing equipment.
• use snow chains on the end of the vehicle with the dissimilar spare tire and wheel.
The usage of a full-size dissimilar spare tire and wheel assembly can lead to impairment of the following:
• Handling, stability and braking performance
• Comfort and noise
• Ground clearance and parking at curbs
• Winter weather driving capability
• Wet weather driving capability
• All-wheel driving capability (if applicable)
• Load leveling adjustment (if applicable)
When driving with the full-size dissimilar spare tire and wheel assembly, additional caution should be given to:
• towing a trailer.
• driving vehicles equipped with a camper body.
• driving vehicles with a load on the cargo rack.
Drive cautiously when using a full-size dissimilar spare tire and wheel,
and seek service as soon as possible.
