Can iTunes reveal which songs are currently on a device?
As I understand your desired functionality, iTunes does not adjust the main library view based on a connected device. You have to select the specific device and see what it contains. 

The closest you can get is to plug-in your iPhone into your computer so it appears under Devices in iTunes. If you click on the little arrow in front of your iPhone's name, you can browse its content easily.



In addition you can also see which playlists, artists, genres and albums get synced in the  Music section of the syncing window.