wherz-
There's a backhanded way to do your experiment- without the experiment. Thanks to Newton, we know the relationship between mass and energy and how it is conserved in a process. A car for example, which is powered by gasoline and an internal combustion engine- wastes about 65% of its energy in the form of heat and noise.
Therefore, if two identical TVs run in a controlled environment, one LCD, one LED lit LCD, and let's say the LED one uses 40% less electricity, it would be relatively safe to say that the 40% on the other TV is wasted as heat, and maybe a slight percentage as extra/wasted light.
Thus- an AC unit would need enough power to remove that 40% of power, shown in the form of heat. I know this over-simplification has holes in it, and it's not 100% precise. It would help to know how the TVs convert electricity to heat- which I don't know. But- I think this does explain the ratio of work the HVAC unit has to deal with on a relative basis.