The only concern I'd have with grapes is that the vines can get heavy as they mature over the years. You'd have to make sure they have good support. Some people build sturdier runs than others, depending on their needs. You can always do a really hard prune if they start to cause a problem, though. Or add a little more support in that area of the run, if you find you need it. The young growth is no problem at all. Other than that, they're great. Their leaves are used in some cooking recipes.
We have the seedless red ones called reliance. They are fantastic eating! Sweet and flavorful. We've got ours planted over by our hardy kiwi vines. Also monster vines, but very tasty. I don't know if their foliage is edible, but I'm not aware of a problem with kiwi foliage.
Darkmatter, your chickens must love you! Yummy!