As far as the quick-hitting bass like Redddog88 mentioned, a second battery won't help at all. As the amp needs power, it draws from the circuit...the alternator provides what it can...if that's not enough, the battery picks up the slack. So the battery says "ohhhhhhhh yooooouuuu waaaaaant moooooore powerrrrrrrr? Okaaaaaaaaayyyyy". By that time, it's too late. The cap will discharge almost instantaneously by comparison. The cap would say, "o u wnt pwr? k!" like Beavis on crappucino. Then the alternator recharges the cap (or battery) between these large power draws.
Think about it this way: you have an alternator, two batteries, a cap, and then all the power consumption devices. You still only have one power source (alt), three ways to store it (batteries and cap) and many ways to use the power (amp, lights, radio, etc.).
Adding a second battery will allow you to run your system longer with the car off, but if you have the ability to drain two batteries with your system, then as soon as you start the car, the alt has to charge two batteries instead of one. THAT's what will strain the alternator.
Screamin Eagle is mostly right...except the alternator has NO delay in providing power...it provides it no matter what, it's just a matter of what devices grab it. Theoretically, if you didn't need a cap but had one, the cap would charge and then never discharge (not accounting for leakage) because the circuit would never need more power than what was being put in by the alternator.
99BlackAlero: your system doesn't really feed off the second battery. It feeds off the entire electrical circuit, of which both batteries and the alternator are all a part. The alternator will always provide as much power as it's capable of into the circuit until more is needed, then the storage devices will dischargeto make up the difference, cap first because of less delay, then batteries. And after the discharge, the storage devices will pull current out of the circuit to replenish themselves.
[edit -- adding a bit more]
If you're concerned about not having enough power, get a bigger alternator. Pushing an alternator to 90% of it's capacity all the time is what'll make it fail. Get a big 200-amp alternator (or at least something larger than what we've got, which I think is 105-amp...not sure though) and let that run at 60% and it'll last forever. Sort of...
Adding a second battery won't hurt anything. Adding a cap will help condition the power so your amp sees consistent power...that'll help the amp's power supply last longer. Getting a bigger alternator will prevent nearly any electrical problem that a system can cause...although if you compete it may change the class you're in since there's more power available to your system. Something to keep in mind if you compete. (I don't compete, so I don't know the specific rules, but if anyone is going to upgrade the alternator check and see if it matters to them...you know.)