However, it is actually possible to do the following...
(in ES6 syntax)
Now, why would you want to do such a thing? I thought the whole point was to use React to tie together your view and logic layers (and shouldn't you be abstracting out your heavy logic to plain JS classes?).
Well, the main reason you might want to do it is because of React's component lifecycle.
In my case, I wanted to trigger some JS to run when the component was loaded, and I happen to be using Turbolinks and React-Rails in a Rails project.
This JS had no view component, but I could not rely on document.ready because of Turbolinks, and I didn't want to put an inline script tag in the page (because who wants to mix JS and HTML together?). I was however happy to use the react_component helper to add in a React component and then trigger it on componentDidMount.
It's also a handy way to add functionality onto some components which for whatever reason need to be rendered by the server (i.e. adding a JS slide show component onto a bunch of rendered divs without having to pass all the images into react_component).