Wireless Internet Signal from "Host Computer"

I know that in most wireless networks, the router picks up the internet signal directly from the modem, and broadcasts that through the air for computer signals to pick up.

However, my DSL modem is from the stone ages, and doesn't have an ethernet port on it to connect to a router. It connects to a computer directly by USB.

So, the question is: Can I broadcast a wireless signal by connecting a router to a sort of "host computer" with an internet connection, rather than directly to the modem?