Going completely on theory here:
Muzzleloader rifle slings are usually attached to the barrel via a tenon on the underside of the barrel. I would think that any pressure on the sling would change the point of impact at least a bit. Having said that, the same issue also applies to the use of a shooting sling on even modern guns guns without a freefloated barrel, including most of the weapons used by the US military since the introduction of the shooting sling (notably, the M-16, which also has a swivel directly attached to the barrel), and that hasn't kept slings from being a useful accessory.
My guess is that the influence of the sling is going to depend on a lot of factors, such as the barrel thickness, how far out on the barrel the sling is attached, and how hard you crank down on the sling. With light pressure and a stout barrel, you might not notice anything, particularly at the relatively short ranges that most muzzleloading shooting is done. With a long, skinny barrel such as is popular today and a tight sling, possibly quite a difference.
I recently acquired a shooting sling, but haven't tried to use it yet, much less on a muzzleloader. I can't imagine that one could be used without SOME change of impact (and the resulting increase of group size from the inevitable uneven pressure on the sling), but the better stability might make for a net gain in accuracy. Only way to find out is to try it, I suspect.