Yes. You can play music from the car's native system. You need to enter the music screen in the upper screen to select and play the music. Once you do so, you can then enter the Apple CarPlay (in my case the Android Auto adapter) screen via the home icon in the upper screen. Once you switch back to the Apple CarPlay screen, the only place you can see what music track is playing is on the right side of the screen behind the dash.
Similarly, if you want to use the native car navigation, you need to switch to the nav menu in the upper screen, select the destination there or via the lower screen, and then switch nack to Apple Carplay. You can see the directions on the right side of the display behind the screering wheel.
The only drag with all of this is that the lower screen doesn't show anything but the car menu when you are looking at the Apple CarPlay portion of the upper screen. So you can't see the native music track or nav on the lower screen at all while the Apple CarPlay screen is displayed.