Yes, this will extend the WiFi network. If you plug the Ethernet cable in and setup the Express it should be able to extend the WiFi network. You want to "create" a wireless network, make sure the network name, password and security type are the same as each other. The security type can be found in AirPort Utility for your current AirPort.
I set up my network as I described above. When I tested the devices that were connected to my Gigabit switch, none of them detected my network. I made sure that the cable from my AEBS was plugged into the WAN port on my AE2 and then I have a Ethernet cable from the LAN port on the AE2 to the GBS.
I went to my local Apple store and they recommended a network extender. Isn't this what I kinda have already?
I'm stumped. Anyone have any ideas.