Yes! There's a basic implementation for Raw Sockets that I used to port node-irc to FxOS: https://github.com/nickdesaulniers/fxos-irc

I would love to have someone fix https://bugzilla.mozilla.org/show_bug.cgi?id=878972

It would be like making a cathodic ray tube with oil paint :-)

But you could write one in JavaScript for FFOS, since it provides an access to raw TCP sockets:

https://developer.mozilla.org/en-US/docs/Web/API/TCPSocket

I'm not sure how FFOS apps work, but the answer depends on how you define "SSH client in HTML5". [1]

[1] https://news.ycombinator.com/item?id=3108453