My impression of the serial to ethernet converters is they do format conversion [RS232 to ethernet (IEEE 802.3, etc) and nothing else. So unless the ethernet converter has the ability to grab the NC file and act as a server for FTP, the answer is probably not.
Nevertheless, have you tried googling around for some that can do what you want?
I know what you want can be done, the question is has someone already done it, or are you going to have to build this yourself?