The 15" spare on the MINI Cooper is stored underneath the boot rather than in it. The picture below shows the spare tire after lowering.

[click for complete pictorial on MINI Cooper spare tire]
You can use this spare regardless of what size wheels and tires you have fitted ... it is only meant to get you to a repair shop [at a reduced speed] to get your flat tire fixed. You may have to order the spare tire as an option on the Chili Pack ... check with your dealer.