Not exactly.
It's more like the router will recognize the desktop, and pass the connection from the modem to the desktop.
The router will not show up anywhere on the desktop, unless you access its setup page with a browser, by typing in its IP address in the browsers address bar.
If the modem is also router, you might need to do some tweaking to get everything working together.
But usually you just plug the modem into the WAN port of the router, and the pc into one of the LAN ports, and off you go.
