I program my HDTV to shutwdown 3 mins in the absence of signal from the PC. I have not tried to set it to zero to automatically shutoff. Technically its possible but i have not than it. I'm not sure if your HDTV has the same feature. Read the manual of your HDTV specifically on Digital Link/PC link.
When my PC goes to sleep mode my HDTV flash a message on the screen informing of lost signal from PC/HDMI link and it counts down to shutdown.
My PC sleeps in situation that there is no task that are set to run. It wakes up on scheduled task. My LCD screen pretty much follow the PC. My HDTV i just turn it on when i need it.