That should be possible! Of course, stateless components don't have state, so you would need to something like Recompose if you need that. And of course, not all React-related projects explicitly support stateless components at the moment (e.g. hot reloading).
Another option is to use psuedo-local state with Redux and pass everything as props: https://github.com/rackt/redux/issues/159. As Dan notes in that issue though, it might be better to wait for the state tree model to be improved: https://github.com/facebook/react/issues/4595.
In short: early days, too early to tell what patterns will emerge.