Only through a computer. You would need the computer in order to be able to connect to the network and share the appropriate resources. The enclosure does not have the software or hardware necessary to do this task. If you did get an adapter that converted USB to ethernet and plugged it into the router, nothing would happen.
^+1 not currently with what you have got, but you can get routers that allow usb HDD to be connected to them for network share!