That would be cool indeed. Current jsdos doesn't support networking afaik. v86 does so you could get DOS running in there and use WebSockets. I've also seen people directly porting dosbox with networking support to run Windows 3.1 with Netscape, in VR. So it's possible for sure.
http://assets.metacade.com/emulators/win311vr.html
If you could reach out to me... tracker1 at gmail ... would appreciate it. Thinking it would be cool to get a couple old BBS terminal programs running in your dostbox js setup... RIPTerm 1.54 as an example... but no idea how to get it to connect to a modern telnet bbs. There are websocket terminals already, but would be cool to get websockets into the jsdos environment.