Idk, I think I'm going to have to disagree. The system gets strained (and lights dim) because the power isn't there to give to the amplifier so the voltage drops and you could basically say the system fails. Adding another battery will add to your available power at any given time, thus supplying more of the power that the amplifier wants and getting it closer to "passing" (instead of failing). Thus the alternator is going to have to recharge twice the amount of power it did before. I mean a battery only has a limited amount of power it can give out before falling below the resting voltage.
Idk, maybe I'm wrong, I'd like it if you could get as technical as possible simply for the fact that I like to learn things...