If you old fob is truly dead, you can simply push the button to release and keep your old cut backup key.For that price, they should at least throw the key in.
Well I tired pairing a loaner CTS-V key I had when the ELR was in for service and I picked up/dropped after hours for funsies and it didn't work. I assume they are different frequencies.The part number is unique to the ELR, but I would imagine something else would program to the car. You could always pick up a cheap one on eBay and give it a shot.