AppleCare ended any value in keeping agreement #
Pretty much AppleCare helps with resale value, but usually only when you have it still active. I suppose someone might presume you meant to take care of your device since you purchased it or may have given it better care and service since that was prepaid?

The agreement number only matters if Apple loses the record, though. Most AppleCare is provided on the basis of the serialized product - not the agreement number.