So, here you have the classic video feedback loop catastrophy clip.
It is from the Pentax K-7 and it is an all digital feedback loop in HD :)
While recording video, I output the live view of the video recording via HDMI to a an HDTV, the one I am videographing.
This is interesting to study the latency between real life and images showing up on the screen.
Note that the recorded sound (from the internal microphone) is played back in the loop as well. You'll hear a subtle echo.
FWIW, the video demonstartes that HDMI output is active during recording. Albeit only in LV resolution, i.e., 640x480.