well id sudjest a battery no matter what. its way hard on the alt to be pulled on without. i have a 220 alt and a 93ah batt and not volt drops on my sundown 2000
so your amp will be pulling current all the time when your music is turned up. At idle the alt will not produce enough amps, at 3000 rpms your alt will produce more than enough. so a battery balances that out so your amp always has enough.
Assuming it puts out exactly 220 amps and charges your battery to a constant 14.4 volts and your amps are 100% efficient and cause no voltage drop at all, it's good for 3168 watts. Power = current x voltage
You'll probably have voltage drop, and your amps are probably 60-80% efficient, so just subtract from there..