You can certainly do that for iOS and Android - I've recently launched an application myself which does just that. At least 95% of the code is shared between platforms.

There are some desktop bindings available, but they're relatively experimental:

https://github.com/ptmt/react-native-macos

https://github.com/Microsoft/react-native-windows

https://github.com/jamrizzi/react-gtk (no code yet, just intent to develop)