It used to, but a few years ago (2019 I think?) they changed so that it's a properly separate display.
The only thing you can't do is separately play audio from the phone (because the CarPlay unit is basically serving as its output while it's connected), or use your maps app to do something different while the navigation is running on the CarPlay unit (because CarPlay is just a view into the phone's apps, and so they'll both be in navigation mode).