How to hook up an Arduino Uno to serial and ethernet
I believe the USART on the 328P is connected to the AT8U2 Micro, which is doing the USB to Serial conversion.  You my be able to use these same pins for another serial device, as long as you aren't connected to USB.  If this is the case, then you should have no conflicts from the Ethernet shield.

If you need to roll your own serial using other pins, just look at the ethernet shield first to determine what pins it is using.