Any battery used in the rear should be a sealed type battery, a wet vented battery will produce vapors that will make you sick.
So in physics class, when you were working with 12V batteries, were they operating at 14V? Thats an honest question.
I will be posting a video - hopefully tomorrow - my buddy has 8 batteries in his house powered by a 50A power supply running a 120A load - according to him it rarely gets in the 12V range. I am taking voltmeter, DC Inductance Meter (Clamp) and video. Will post that hopefully Sunday night
Then later this week, I will demonstrate what this does in a car with 1) stock battery and 2) added battery in rear using dual clamp meter, dual voltmeter. One of each meter in the front, and one in the rear along with dual video so it can be captured and then editied to play side by side. I have a third clamp meter to show ALT output as well
What I expect to find out of the second video - the rear battery will discharge at a higher rate then the front battery and keep voltage higher. Why do I expect this -
DC resistance of the cabling at 18ft VS DC resistance of cabling at 2ft. All cable will be Kolossus and ran on the outside of the car. Batteries will be fully charged by a trickle charger before hand and between the two tests so that eveything is equal. Signal will come from a tone generator. All meters will be checked to verify readings match before test begins so that not a single question can be raised or suspect.
Vehicle is my POS DD that at one time was used for DB Drag, it has been gutted for the most part making it easy to do this with. Alt is a 90A Ford unit, and the amp will be a large Class AB amp (might as well use something that isnt efficient to show worse case IMHO)
My point - a HO Altenator is helpful- not everyone can get one for there car, not everyone can afford one, but there is no replacement for the reserve capacity of a

Battery(ies) espically when mounted inches from the demand. And the additional batteries will serve no additional strain on a properly working charging system.