I'd say, "it depends" on the slave's firmware implementation of Modbus.
The slave's data is in the Modbus registers, but the question is whether the slave will respond to both a serial port request and a TCP (ethernet) port request, which is a slave firmware issue.
Just because a device has an ethernet port, doesn't mean that the Modbus is accessible via ethernet.
It would be very easy to test with a PC running one of the Modbus Master simulator programs, like Modscan32, or Simply Modbus, or Modpoll, configured for Modbus TCP on the ethernet port.