It's not like that at all - alternators turn freely, their output is related to RPM.
Under cruising RPM, your engine won't "work harder" to generate the power needed to run the miner, that power is already being wasted in the voltage reg/charge systems. Miner is drawing from the battery, alt is providing variable charging amps to the battery/+ circuit while running. Simple, keep the charge rate > discharge rate.
Nope. That's not at all how alternators work. There's no "extra" power -- the voltage regulator found in every single alternator-equipped car is varying the excitation current in the brushes of the alternator in order to get a relatively constant charge at the battery terminals. The more load you draw, the harder the alternator will have to work to replace that load, all under control of the voltage regulator.
For instance, drag racers -- who are trying to eke out fractions of a second over their competitors -- use techniques such as electric water pumps and electric cooling fans that they can turn off for the duration of a run (less than 10 seconds, generally) and then turn back on again to cool down the engine once the run is complete. They don't do that for shits and giggles, they do it because it reduces the load on the engine, which allows them to deliver more power to the wheels.
(And in
serious drag racing -- well above the hobby racer level -- I wouldn't be surprised if they did away with the alternator altogether and just used a battery).