Ethernet and WiFi hardware co-existence

Hello all

Arduino virgin here.

I am creating a DUE based project. But I would like to know if WiFi and Ethernet hardware can co-exist within the same project.

So if there is no WiFi an Ethernet cable is plugged in and all communications is via that connection (this should be an automated feature). But if there is WiFi then a connection is made via that and all communications are via the WiFi with the Ethernet disabled. So it is one or the other network connection.

Yes I do realize that there will have to be some setup for the network connections. As to how I will achieve this I guess will be determined by the finished hardware selection.

The UI for the project is web server based.
The project has a 7" SainSmart touch screen for human interface.

The SainSmart screen and the DUE are already the basis for my project as they came as a kit and that was the sized touch screen I wanted.

Your guidance will be most helpful in this early hardware selection stage.