No, when you use the modem connected on port COM RS232, OMNIAlog is configured (through its webserver) to transmit the traffic on serial port. This could cause connection problems if you connect the PC on the LAN port of OMNIAlog.
To use the communication on LAN port, it is necessary to disconnect the RS232 cable (or from OMNIAlog or from modem) and reboot OMNIAlog. OMNIAlog, at reboot, tries anyway to communicate with the modem through the port COM RS232 but it doesn’t find any answer, so the communication is transmitted on LAN port.
When the activity on LAN port is finished, it is necessary to do the opposite procedure: disconnect the LAN cable, connect the RS232 cable (and so the modem) and reboot OMNIALog. At reboot, OMNIAlog tries to communicate with the modem and, finding a valid answer, transmits the communication on serial port.