You can write a network device driver, which exports the network packages into JavaScript. The author already wrote a console device. So, not much of a deal.
Doable for http and https, but if you're running it in a browser environment, you'll eventually run into issues with CORS and other protocols. To get around this you need a proxy server running elsewhere that exposes the lower layers of the network stack.
This is exactly what [0] does. Try it out. If you know the IP you can even log in to another open browser window via telnet.