Yes, I would do that. For me, it would be comforting to know that my beloved pet spent their last moments in their own home. I know that might not always be possible, if the pet is already at the vet's office and is in pain and suffering.
Call and talk to your vet about it. He or she will most likely be willing to work with you.I've never heard of vets making "house calls" here in MD to do it.