Steve:
I assume you're thinking of shooting slugs on game, right? The answer, unfortunately, is "it depends." A shooting sling of any kind is awkward to use with slide action shotguns, so mostly we're talking about break-action and semi-auto shotguns, and probably mostly the latter for hunting with slugs.
Hypothetically a shooting sling, including the Safari Ching Sling, could work on a shotgun just as it would on a rifle. But, just as with rifles, some designs are more resistant to changes in point of impact due to tension on the sling when the sling is used for shooting support. So, I"m afraid you'll just have to try it with your particular shotgun to find out.