not really, no. If you want to run the system for prolonged periods at high output with the engine off, I would recommend a second, isolated battery for the audio system so your starter battery doesn't see the audio system, though.
Horses for courses.
The alternator will supply current when the car is running. The battery does this when the engine is off. For engine-off usage, on a second battery, go with a large deep cycle battery. The discharge hysteresis curve is ideal for this, though they do take longer to recharge.