If you shop around, you can probably find the Linksys router for about that ($140 of you need the 4-port switch).
It would be possible to detect that more than one computer was involved. The router uses "single address NAT", and sets the originating port address uniquely for each workstation so it can route the replys. That means someone could analyze your packet stream and see that more than one computer was involved because there would be multiple port addresses and they would not be standard port addresses. I doubt cable companies do that.