Salt would only add flavour to the bits that are going to be thrown out. In this case, you want all the flavour to remain in the liquid so definitely no salt.

I usually make chicken stock (carcass + carrot + onion + celery if available) in a pressure cooker. I found long ago that this way, the bones ended up all crumbly and harmless, and the strained remains could safely be offered to the cats who were trying to break down the kitchen door. This avoided a disposal problem - we had paper waste sacks at the time, and any wet waste had to be wrapped in lots of newspaper.