Hi Jim,
It is my understanding that a BB1 can RECIEVE YouTubes video and YouTube music and then play the vide on its screen and sound on its speaker. I do not believe that the BB1 can onward transmit the video to a second device.
It would seem to me that if you want to watch YouTubes on a TV there are a number of ways of doing this, either form a YouTube app on a smart TV or bu inserting a smart HDMI device (eg a Fire TV stick) into one of the TV's HDMI ports.
Fred