EMC testing of devices with Ethernet
No, this is not a valid test case. A valid test case would be with both jacks connected to a router or switch. You should do high data rate transmission from both ports (somehow), since when your device is transmitting over Ethernet, that is the worst case scenario.

Please also note that emissions on the Ethernet cable may arise from any circuitry on the PCB, not only Ethernet PHY activity. Cables often become transmit antennas for any frequency clock (or harmonic) on the circuit board.

For example if the processor clock is 128 MHz, you may see radiation at 128, 256, etc any time the cable is plugged in, even if Ethernet activity is disabled.

As a means of debug, it is good to have the ability to turn things on and off. For example if you are failing, you can turn the ethernet transmit function on or off to see what difference it makes. You can also plug and unplug the cable to see what difference it makes, etc.

Often, the people who run the lab where you do the testing can provide advice about how to set up for the test (they may be able to provide you with a hub or router you can connect to your device). There is far more to it than can be covered in a short answer like this.