true...however if your voltage is over 12 volts you have little to worry about. The chips in car amps are created to operate at low voltages, so it'* not a like a 40 volt chip in your reciever that only gets 30 volts, and still sounds good, but isn't operating at it'* most efficient.
The amperage, or current that your battery can supply over time (not peak....we all know 600 CCA is more than efficient for a heavy hit) is very crucial. And the current/drain curve would neat to see. Of course, I'd suppose the voltage drain curve would be neat to see as well.

I've never messed directly with car audio amp chips, but if they're like high power amp chips used in recievers, they're pretty lenient in the voltage they recieve. I'd guess that a reciever would work fine on 8 volts (assuming voltage protection circuitry doesn't keep the unit from powering up).

A small drop in voltage is going to have a direct effect on amplifiers. Although the wattage is measure I squared R the I is from the voltage applied to R. Thus the term half the voltage quarter the wattage.

Look at some amp chip specs...most notably, the voltage/max wattage attainable. It doesn't quite work by an equation, unfortunately, mostly because audio amp chips accept a wide range of voltages, and therefore have some regulation going on. In theory, however, you would be right.

Keep in mind what class amp it is. That is going to have a big impact as well on the power output. I always try to stick with Class AB or D amps.