No. The greater the electrical load placed on the alternator, the greater the parasitic load on the accessory belt.
That being said the amount of electricity, and thus the load on the belt, to run the fan is very very tiny compared to the energy required to heat the air. In an ICE, the heat energy is literally free. You were going to dump it anyway, might as well be into the cabin.
I agree with siblings that we're not talking about a significant effect on mileage, but technically there is still an effect. When the ventilation fan kicks on, this will be an additional current draw. Since the voltage regulator is an analog device, it will respond to the resulting slight dip in system voltage by increasing the alternator field strength slightly. The engine will then have to apply slightly more torque to the alternator, which will burn slightly more fuel.
Since engine speeds vary greatly, having a dumb alternator that provided power scaled in proportion to RPM would be a disaster.
That's not how a generator works. Take a DC motor and spin it with your hand and it'll generate a bit of a voltage potential across the terminals on the motor. If you short those together and then try to turn the motor you'll notice that it's significantly harder to turn.
Not exactly... the alternator provides "up to" a certain amount of electricity, but as more of that electricity is actually used for things it gets harder for the engine to spin the alternator and so you end up using (slightly) more gas.
The alternator (or really any electric generator) has a magnetic field, and a lot of coiled up wire. Moving the wire thru the field generates electricity, the faster the wire moves the higher the voltage is. But the more current is moving thru the wire (more load, more things using the electricity), the more it pushes back against the magnetic field (because that current in the wire generates its own field) and so the harder it is to make it move.
That being said the amount of electricity, and thus the load on the belt, to run the fan is very very tiny compared to the energy required to heat the air. In an ICE, the heat energy is literally free. You were going to dump it anyway, might as well be into the cabin.