React follows an approach similar to ReactiveCocoa (https://github.com/ReactiveCocoa/ReactiveCocoa). It helps modularize the code into components instead of having a spaghetti string mess that often happens in view controllers.
Currently there is no details on React Native, however, I don't believe it would replace the Storyboard as views are still necessary for the React code to interact with the components.
What you would be doing is coding in JS and behind the scenes your app would interact with the views and do the necessarily updates. I'm guessing it'll be a hybrid approach. While you'll most likely still need to know Obj-C or Swift, you can probably get away with a lot of boiler plate code with React.
Having a brief look over the ReactJS webpage, it seems like it would replace view controllers and perhaps Storyboards?
Or are we talking about writing the entire application in Javascript, declaratively?