I assume the "shooting sling" which Der Ami is referring to is a sling that you strap around your elbow as to stabilize the rifle when shooting. Sort of military offhand style.
I agree that this use can goof with your accuracy on a double but you won't really know how much until you try it with your rifle.
Generally, a sling on a double is for carrying not shooting.
I suspect that this is why so many original heavy doubles came with wide canvas strap slings.
Every double rifle I own or have owned has had sling swivels - I'm thinking they are there for a reason.
