I see no reason why a muscadine vine wouldn't grow on your fence, but with age the vines get really big and when loaded with fruit they are quite heavy. If your fence can handle the load, sounds like a perfect cover crop to me! Take a look at Ison's Nursery & Vineyards to see if they have anything that interests you. Their catalog is free and full of excellent information.
I'd be happy to send you some seeds from my wild crop later on this year if you don't have access to some in your area.
Ok, I have to ask, what are critters with no shoulders?