Where does this article talk about >1s connect times for websocket? The websocket handshake is a single network round trip (discounting any added by TLS if you are using it) and the initial client message frames can be sent in the same TCP packet as the handshake. A websocket connection should not add any more latency than HTTP(S) connections.
WebSockets don't have much startup time at all really. If you're using Socket.io or another Flash-based abstraction you can expect long lead/start up times due to the Flash policy file, but plain old WebSockets should be as fast as any other TCP connection.