In pure dc voltage never ever, only thing that can happen is that the output voltage will fluctuate + - 0.3 volts, on the other hand the 470uf cap helps to compensate for this.Just one detail - why using a zener diode, known to be noisy, in such application?
with normal power supplies, dc voltage from ac I agree, the zener can be loud, but only if you forget the rc filter at the zener diode output.