gonna have to disagree with that statement. That it is a "digital amp" is almost irrelevant. You certainly don't want actual '1's and '0's going into your speakers -- will sound terrible. Anyways, yes it all will be analog in the end, even if the amp is class D and is using PWM. But supposing it were dumping '1's, you certain CAN make the 1s "stronger" -- the pulses can be 0.1watt, or 1watt or 10watts or 100watts (divide by E or I if you want I or E).
In this case, since car audio amps are designed to run off of 12V, it is I that matters (current). A powerful car audio amp can draw quite a bit of power, and given 12V, therefore current, upwards of 50A or more. So it matters whether the 12V power system can supply the currents needed. If the lithium battery has greater capacity, it will certain make for louder music, especially the bass notes. Capacitors can help by delivering added current for short intervals (smoothing out voltage spikes by supplying current).
In high powered ICE car audio systems, the alternator often determines the max power (current since its all 12V) available and folks install higher capacity alternators just to have more power available for their sound systems. Of course if the sound system is only a measely 10-20 watts, its not going to make any difference...