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Bad news:
If you use your spare, no it will not hurt. However, a spare that is never used, will be affected by UV and ozone and will eventually start to crack. The flexing of a tire, causes the carbon black and other adatives in the tires to condition the tires as you drive. A tire cover helps to protect the spare from ozone and UV light.
Last year, NHTSA and the tire industry, recommended that the auto manufacturers start printing information in owner's manuals in regard to spare tires and they should be replaced after 10 years of non-use. However, this recommendation was for spare tires in the trunk; those subjected to UV and Ozone might degrade faster.

Good news:
It will take many years, depending on the conditions where you live.