Yes this can be done, but the tools necessary to do this are buggy.
I am using the Windows Version of Airport Utility, and perhaps the Mac version is not the same, but these steps likely work for both.
Once you turn off the Wi-Fi in the airport express, you can no longer discover or reprogram the AirPort Express on the network with the AirPort utility, even if it is working perfectly.
So the methodology is to set the AirPort Express up like you are creating a new wireless network connected to the network. I used a different name for that new AirPort Express wireless network than my main wireless network for testing purposes. As you create this network, make sure that ultimately the connection sharing (found under the internet tab is off (bridge mode))
You can test this network by joining it wirelessly and making sure that it is seen by airplay and is working well. Once you have done all the testing you want, you are ready to turn off the wireless transmitter.
You do this by going to the internet tab in the airport utility, and you change the wireless mode to off.
When you update in the AirPort utility, you will no longer be able to scan and find that base station using the AirPort Utility, but it will actually have programmed the WiFi off and the Ethernet will still transmit the signal to the AirPort Express. The ITunes speaker name that you set up earlier when it was wireless will be displayed in the Airplay device, and can be accessed like all other airplay devices.
Oddly, the iOS Airport utility will tell you that all is working, and the green light will be solid, but the Windows AirPort utility will no longer find that base station to reprogram.
As an aside the iOS AirPort Utility seems to communicate with the base station, but when I turned back on the wireless signal, I could not communicate with the base station. At that point I had to do a hard reset and start over.