Nil,
The capacitor reserves up "burst power needs" that an amplifier would need from time-to-time (typically heavy, loud bass passages). It has very little to do with a speaker, including a subwoofer speaker. Unless the JL Audio Stealth Box includes an amp AND includes an internal capacitor - then the guy you talked to doesn't know what a capacitor is. Or maybe he thought you were talking about a crossover.
JL Audio is a good brand of subwoofer speaker. I have a pair in my MB.
I'd definitely talk to a few other shops (if possible) and start getting a good handle on the terminology and products available. There are MANY paths and price ranges you can take to improving the sound. I'm not sure how much better you want the sound to be. Many shops THINK you just want louder and more bass (to make your car a boom-box). Personally, I HATE these. The overall purity of sound is horrible. The bass IS loud, but often distorted.
And you can pay lots of money and get just that. So be sure to tell them your budget and what you want it to sound like.
I went for a clean-installed look, and audiophile sound quality. My components are: Kenwood front-end, Kenwood CD changer, Precision Power amp 50watt x 6 channels, MB Quart 6 1/2 inch speakers with crossovers and separate tweeters, and 2 JL Audio subwoofers in a custom-made box. Each speaker has an amplifier. I have no capacitor. The sound is unbelievably clean, pure, and can get quite loud when necessary (top-down, passing that 18-wheeler!). It can crank out overwhelming amounts of bass, if desired, too. It was pretty expensive (over $2500), but I got exactly what I wanted. Pioneer, Alpine, Kenwood, Clarion - there are many good brands of head-units out there - same with amps. Compare features (that you'll use) and performance. Ask around. Different shops will tell you different things (usually because that's what THEY sell), but you'll start to develop a sense for the good stuff.
I have decided to leave the sound in my HCH-II alone - for now. Since I have the NAVI, I'll probably never change out the head unit, but I could upgrade the speakers, add an amp, or add a sub.
The best low-cost improvement is usually the speakers (the ones in the doors and rear deck). You can even replace the rear deck ones with small subwoofers, I suspect. I think the Honda Bass Kit is just that, with a small amp just for them too. Next up, would be to add an amp, to give these better speakers more zing. For many people, this is as good as they want. And it's usually quite good. High power amplifiers can draw a lot of battery juice. That's one reason for a capacitor. For the Hybrids, another reason (I think) is so that the power demands of the high-power amp will less-likely interfere with the hybrid battery's other demands.
Tbaleno has a kicking system in his HCH-I. I'd read up on some of his posts. I'm sure there are others.
I could ramble on and on...