As long as the AC input signal is within the linear range of the amplifier, its effect is to modulate the base bias.
That base current can never be zero (or negative), or so high the transistor is fully on, as long as the amp is in its linear operating range.
The average current through the base bias resistor will be close to its no-signal value and a fraction of the load applied by the collector circuit.
I cannot see any possible way the input signal could adversly affect the battery, other that applying voltages vastly beyond the normal signal range.
With the linked example circuit the transistor would likely fail before a high level input signal had any undue effect on the power source!