There’s nothing stopping it from being used on big projects; but as far as best practices go, something like Redux is more strongly tested, middleware-extensible, and will maintain a separation of global state and view layer.
ReactN does not currently officially support server-side rendering. There are very strict limitations on what is possible with SSR. It is an intended future feature, but not fully implemented yet.
The biggest disadvantage will be the tight coupling of the global state to React itself. This is primarily a problem for large or long-lived applications that may desire to change frameworks as time progresses. One-off, small, proof of concept, or personal applications are the intended audience, where the tight coupling provides greater advantages through less boilerplate and learning curve; but many believe this to be an overall disadvantage when it comes to enterprise-level applications.