In general, a popular approach for simulating a browser listening on connections is to listen to them on the server, and then use comet , a lengthy poll , AJAX reverse, or a similar method of pushing messages from the server to the browser.
Thus, you remain within all the rules and restrictions, and you will do what has been verified and verified for a long time. It even works through firewalls, since technically it is still the browser initiating the connection to the server.
Obviously, this is not the same as listing TCP connections, but it may be an option for you.