A cap is essential when running a demanding subwoofer, if you listen to music loud and the subwoofer is either a difficult load/small box/inefficient then a cap will be very necessary indeed as it can store enough power to supply the amp when the resistance drops... in most modest systems, they really arent needed. When you start talking about a "500w amp" this means sh*t to be honest, a 500w Boss amp is nothing compared to a 500w Phoenix Gold amp - though they ahve one thing in common neither deliver 500w!!!
As for your system, you should calculate the amount of current yur amp will draw (should be in the manual for a Pioneer) and compare it to the alternator in the car....of the amp draws more than the alternator gives, you ahve a problem, a split charge system with a battery in the boot is the best way, and (see above) possibly a cap. I would have thought that most standard alternators could handle anything a Pioneer can throw at it...I used to run 3 Rockford Punch amps from my Rover and they worked fine....