CocoonJS does offer support for async WebSockets (and 99% of WS usage is async), but my understanding is that it can be fiddley to get it to work properly. The nice thing about Socket.io is all of the fallbacks that it offers if any one protocol is not supported, all the way down to Comet long-held requests.
If you already own C2, why not try a simple test, like one button to press in the client to send a message to the server, server creates a random string and reports it back to the client where it is displayed?
I would be interested to know the results :)