I have not flown the 747. I am typed in the 737 but most recently I have been flying corporate jets. Some of those jets have an electrically driven air conditioner. When it activates, you can definitely see an increase in amperage, so I assume there would be a slight increase in fuel flow, but it doesn’t show on the fuel flow gauges. The other corporate jets I fly have what is called an air cycle machine. We shut the air conditioner portion of it off at 18,000 feet. At that point we are trying to heat the air for creature comfort, not cool it. Temperatures in the upper flight levels are easily minus thirty to minus fifty centigrade.
The combustion engine charges the high-voltage battery and the 12-volt battery, as well as propels the car too. The car gets 40+ MPG overall, but the combustion engine alone only performs at a max of 20 MPG because it's energy is also used for charging the other batteries.
The more that I run the a/c in the car, the less MPG I get because the engine is spending more energy recharging the batteries (and consuming more gasoline), because they drain faster with the a/c on than when the a/c is off. That means that less gasoline is being devoted to propulsion.
In jets, especially during times of high fuel prices, what I read was that running the heaters for creature comfort used more fuel than running the heaters at minimum comfort levels until someone complained. I guess the question is whether the extra fuel consumption is noticeable or negligible.
-PJ