According to the documentation, only .wmv format is supported, and even then it must be encoded using a limited set of parameters.
From the link:
1) Video enabled with Digital Rights Management cannot be used.
2) Video must be encoded to the Windows Media Video 9 "Main" profile by using the VC-1 standard.
3) Video must be encoded with a constant bit rate (CBR).
4) Video must include an audio track.
5) Audio accompanying the video must be Windows Media Audio (.wma) encoded, with a single-pass CBR format.
6) XNA Game Studio supports the following maximum bit rates:
Profile Level Maximum Bit Rate Representative resolutions by frame rate
Main Low 2 Mbps 320 × 240 @ 24 Hz (QVGA)
Medium 10 Mbps 720 × 480 @ 30 Hz (480p)
720 × 576 @ 25 Hz (576p)
High 20 Mbps 1280 × 720 @ 30 Hz (720p)
That's not to say there isn't possibly some clever way to stream the video from YouTube, convert chunks of it to .wmv with the required encoding as they stream in, and load those chunks to the content manager, but it's nothing that would be supported by the framework, and sounds like a lot of work for a problem that probably has a better solution.