You can... but I have a feeling that he's looking at an "economical" shared hosting solution.
With a VPS/Dedi you have full control (usually - I don't know about "managed ones" since I manage my own) over the ports that are allowed.
WebFaction supports websockets on shared hosting. It's a bit more expensive than your junk GoDaddy or HostGator plan but it's worth it. You can run anything you can compile from source and you can open firewall ports to run stream connections.