I’m pretty sure anything you’ve seen promoting React as being good for SEO has to do with being able to render the requested page on the server, before sending it to the client. So it will be indexed just like any other static page, as far as search engines are concerned.
Server rendering made possible via ReactDOMServer.renderToString. The visitor will receive the already rendered page of markup, which the React application will detect once it has downloaded and run. Instead of replacing the content when ReactDOM.render is called, it will just add the event bindings. For the rest of the visit, the React application will take over and further pages will be rendered on the client.
If you are interested in learning more about this, I suggest searching for “Universal JavaScript” or “Universal React” (formerly known as “isomorphic react”), as this is becoming the term for JavaScript applications that use a single code base to render on both the server and client.