A couple of things and I'll preface this by stating that all I know about WebSockets, I read in the past five minutes.
WebSockets are part of HTML5. NET+OS's web server (AWS) is based on HTML4.01.
I do not find the term WebSocket in the code base meaning that in NET+OS's AWS implementation, tehre are no HTML headers for dealing with WebSockets.
In NET+OS if you start the web server, it opens a passive TCP port 80 socket, so all TCP port 80 messages will go to it.
If you set up a CGI page, all TCP port 80 messages still go though the web server before being passed to the user defined function have handling CGI pages. Mow I believe you can get the incomming headers when in CGI mode, but I believe you have no control over outgoing headers. I believe this would be an issue with communicating back to the client.
The only thing I could imagine would be that you'd have to not run the NET+OS web server and instead write your own
thread, sitting on TCP port 80 to act as the WebSocket web server.