As I recall, the factory spares on these trucks is always a smaller diameter steel wheel and regular tire combo.
I am certain this was done mainly due to cost.
GM probably saw no reason to include an alloy wheel and a more expensive tire as a spare.
The factory wheel for my 2004 EXT is 17" with P265/70R17 tires and the spare is a 16" steel wheel with a P245/75R16 tire.
My spare appears to be the factory original tire and I have only mounted it to do some tire noise testing.
The circumference of the regular road tire and the spare tire are going to be practically the same, so there should not be any drivability issues when the spare is mounted.
The sticker on the driver's door jamb will list the factory wheel/tire sizes for the road tires and the spare tire.
Owners that have upgraded their disk brakes have had to make sure their small diameter spare tire wheel would fit the upgraded brake system.
This was more of an issue with first generation Avalanches, though.
The only issue I saw when I had my spare mounted while I was attempting to find if I had a noisy road tire, was the tire air pressure system error I got until the regular wheel/tire was remounted on the truck.
Personally, I would not bother mounting a regular alloy type wheel and tire under the truck as a spare because whatever you have under there is going to get very dirty, regardless of where you normally drive the truck.
Also, the spare tire host itself is not going to be as friendly to an alloy wheel as it is to a steel wheel.
I would only consider tossing a regular road wheel into the bed of the truck when I had a flat until I got that tire fixed or replaced.
I would not mount one of my alloy wheels onto the spare tire hoist.
I do not off road at all and every time I have dropped the spare, it was very dirty.
I usually drop my spare, clean it up and clean and lubricate the hoist mechanism every spring before our summer driving season.
I always recommend at least an annual spare removal and hoist clean and lube so that you are sure how and if that system is working properly.
The hoist on these trucks has a reputation for not working properly when you need it the most and learning how and if it is working is not something you will want to do on the side of a busy highway in a storm at night.