can I use react navigation and redux while keeping them separated?

I am trying to write a react native application making use of both redux and react native navigation. However, I do not actually want to save my navigation state in redux. So I just want to keep them separated from each other. I currently have the StackNavigator and that is wrapped in a connect which then is wrapped by the provider.

const mapStateToProps = state => state;
const mapDispatchToProps = dispatch => dispatch;

// need this Higher Order Component so you can pass properties through the root stack
const AppContainer = connect(mapStateToProps, mapDispatchToProps)(RootStack);

export default class App extends Component {
  render() {
    return (
        <Provider store={Store}>
          <AppContainer />
        </Provider>
    );
  }
}

Is this implementation possible?

Yes, this is possible, and in fact, encouraged.

Quotation from react-navigation docs:

Some folks like to have their navigation state stored in the same place as the rest of their application state. Think twice before you consider doing this, there is an incredibly good chance that you do not need to do this!. Storing your React Navigation state in your own Redux store is likely to give you a very difficult time if you don't know what you're doing.

By default, Redux and React-Navigation have nothing to do with each other, and in its next release (Fall 2018) support for integrating React-Navigation into your redux state will not be documented or encouraged at all.