A battery is a strain if it is weak, amperage draw comes in surges and spikes (since bass is not constant - neither is the demand for current) Unless you are doing DB Drag as you roll through the streets, a second battery will help maintain your voltage during spikes due its reserve capacity. Spikes are what cause most problems. And why do the large DB drag guys use batteries? they have limitied ALT output compared to demand. It is all about reserve capacity.
A battery is a strain if all you constantly do is listen to sweeps and the ALT can not keep up with the draw. Anytime there is no large current draw - your ALT is recharging you batteries. That means between beats, between commercials, between tracks, reloading the changer, talking on your cell, ordering taco bell...etc.... unless you have a constant draw 24/7 a second battery is helpful.
While I am not saying you should not get a new ALT - I am saying two same sized batteries of equal charge and having a properly wired and working charging system, will work fine for 90% of systems out there