Just thinking out loud..
HDMI input always takes precedence over other inputs, so you could not do this if you use HDMI pass through, I.E. pushing your video through the HDMI as well as sound for your "TV" watching through the Denon.
Now if you hooked the HDMI directly to your TV and only put sound through the Denon through say optical or other means, then you could control whatever you wanted and have TV with no audio and have an MP3 play instead for example. Note: Your TV or the device connected through HDMI to the TV would need to have a way to not send audio through the HDMI to the TV and only send it to the receiver, but I think most devices have this function if they let you send audio through another source than the HDMI.
Hope this helps, and if I am wrong perhaps other audiophiles can tell me if I am on the right track.