If the communication card is a "Colnago" 100 Base T connection capable card, then it is possible to connect to both simultaneously, provided that both networks are using the same subnet mask. This means that they can work simultaneously, but can't work on different networks. It is impossible to control which network the meter will send data to if the fiber and the ethernet are connected to different networks.
Meters with Colnago cards can be visually identified; They have a green outline around the ethernet port.
The older comm card, with fiber and ethernet, does not have this capability as it does not have an Ethernet, fiber switch inside the comm card, so in this case, if the fiber connection is made then the RJ45 connection is ignored.