No.
Car wiring is radial from the battery to alternator and from the battery to load. The impedance of the battery is much lower than that of the alternator radial circuit - thus transient currents will be met almost entirely by the battery.
You may like to think what effect the starter motor has on the alternator.
Also, the energy stored in a capacitor depends on the capacitance and on the square of the voltage. Rather than have a 1F capacitor on the 12v line, it would be much better to go to the higher voltage power rails of the amplifier and stick beefy capacitors there.