Noooooo... not quite.
The regulator turns the alternator on or off based on the voltage coming out of the battery. All the electronics run off the battery, hence why you turn the batter on and use the radio while the car is off. The regulator's jobs is to "sense" when the voltage coming out of the battery dips below a certain amount, normally under 13.5 volts. When it dips below the regulator say "oh ****, we need more magic pixies to refill the battery!" and it turns on the alternator and recharges the battery to the 14.5 or so volts. The alternator generates the same amount of AC current any time it's on.
No different than a shop air compressor. Set it to xyz PSI, do some wrenching, drop the pressure and the motor kicks on to fill up the tank again. The air gets filled up at the same rate no matter how empty or full the tank is.
Okay, I freely admit that while I'm a decent shade-tree mechanic, the electrical system is very definitely my weak area. That said, based on my understanding, I think you might be confusing voltage and current. Yes, the voltage is constant (more or less), but the current varies according to demand. Voltage is analgous to pressure, current to volume, in your air compressor analogy, it always produces 100psi, but will vary between 10 and 20 CFM, depending on load.
The primary functions of the battery in a car are (1) to provide initial power for the starter motor; and (2) to provide the initial excitier or field voltage necessary for the alternator to work. Once the engine is running normally, the alternator becomes self-sustaining. Yes, you can run all of your accessories off of the battery, but that's a result of the parallel circuit design of the battery installation.
If your car is running during the day, with no lights, heater, AC, stereo, etc, then the load is pretty much only that required by the ignition system, let's say 5 amps (just picking a number out of the air). To produce that 5 amp output the alternator requires a 1 amp exciter current. This is all done at (about) 13.5 volts, but if all of a sudden you turn on the lights, the AC, and the 8,000,000 watt bass-boosted stereo in the trunk, the demand might jump from 5 to 85 amps. That 85 amp output requires, let's say a 10 amp exciter current, as the exciter and output currents rise, the strength of the EM field in the alternator increases and with it, the resistance in the alternator, hence the reduction in fuel economy as load/demand increases. <-- As I said, that's my understanding. I was wrong once before, it
could happen again...