I think a lot of manufacturers put a dry clean only label on just so that you can't sue if you wash it. We used to put 'Hand wash only' labels in stuff we had made in India as a bit of a get out clause.
Given the state of the cushions, I would probably chance it. I'd soak in cold/luke warm water with stain remover for quite a while, maybe overnight, but keep an eye on it at the beginning.