It can be used for that, but it quickly becomes cumbersome. Redux, in my opinion, should be used for complex UI state in applications with complex interfaces where interactions with one part of the UI can change very different parts ("spooky action at a distance", so to say). But it shouldn't be used to keep all your application's state.
Your application's state should live outside of React, and be passed in as the root's props.
I agree w.r.t. what you should Redux for. That said, if you store application state in Redux, is that nout "outside of React", passing it in as props? (Though not necessarily the root's props.)
Your application's state should live outside of React, and be passed in as the root's props.