* Chrome supports it
* Firefox supports it in Aurora and Nightly, not in Stable yet
The support for HTTP CONNECT with TURN-TCP and ICE-TCP is included in the Google codebase.
If you are really talking about unit tests you can take a look at the patch we sent for Firefox:
https://bugzilla.mozilla.org/show_bug.cgi?id=949703 Unit tests are very implementation specific, those are nICEr unit tests(nICEr is the Firefox ICE library).
In addition I recommend you to test the most common network configurations of your partners (authentication, blocked ports, pac files...).
Regards,