Not aware that the TCS supports direct streaming, maybe the Cisco MXE platform, but do not know it for now.
What I would consider do is to use a Codec like a C40, use a HDMI capturing hardware
(like blackmagic) which works together with a youtube compatible streaming software (like wirecast).
Depending on the resolution / quality demand, if multiple resolutions are needed you might
also some bandwidth to the youtube server, but sure thats less than 100.000 streams to your own server ;-)