Yes MSIE11 supports TLS V1.2, 1.1 and 1.0.
Use WinHTTP or WireShark to inspect the communication via browser and webserver.
You should be able to tell if your proxy / firewall is hindering communication, or if the browser is using (handshake negotiation) to request a (different encryption channel).
Without more information I can't troubleshoot your specific problems... A lot improved in (Win 8.1).
