Can carpet scraps be used to repair existing carpet?
Yes, a skilled flooring installer can patch in carpet to repair damage. It needs to be oriented with respect to the "grain" and pattern-matched. 

Chances are you won't want to do that more than once or twice during the life of the carpet, since worn carpet tends to appear quite different from new carpet, diminishing the value of the repair. If you're a careful person you won't need to have repairs done often anyway, and if you're not you'll have too many stains to bother repairing any.

I'd only keep two or three of the largest scraps. Use the rest as utility rugs or recycle them.