Can an amplifier charge itself?
Without a separate power source, no.

You cannot create energy out of nothing. Your device that takes 1A as input and provides 100A as output can work one of two ways:


It can work as a transformer, reducing the output voltage so the power stays the same. Power supplies do this - take, for example, 230V/1A and provide, for example, 23V/10A.
It can use a separate power source to provide the output power. Audio amplifiers work this way - take low power signal AND power from the mains or a battery and provide the output.


In both cases, the total power output from the device is ideally the same as the total power input to it. In reality, the device itself wastes some power as heat and you end up with the total output electrical power less than the total input power. The difference is the heat power dissipated in the device.