A running WebVI built from G Web calls into the browser that it is running on for outbound WebSocket support. Modern browsers should have support for secure WebSocket connections and because the support comes from the browser itself there are some settings, like using self-signed certificates, etc. that would have to be configured at the browser or operating system level and not the WebVI diagram level.
The Connect WebVI to WebSocket Echo Server example has a demo that shows connecting to a secure WebSocket server (notice the wss:// prefix in the URL) to send messages that are then echoed back over WebSockets.
