Might be inaudible for the first few db, but far from inaudible once you are 30 or 40 db attenuated.
Actually not - as you turn down the volume you effectivly reduce the signal against the quantisation noise floor, without turning down the noise floor.
However, if you cannot hear the noise at the amplifier gain/voluime setting you use accross the digital volume range, then you can't hear it.
It doesn't matter how much you turn down the volume digitally - if the amp gain stays the same you still cannot hear the noise. Youve reduced SNR, but by reducing the signal (which is what you want to do) not by increasing the noise.
As long as you are unable to hear the noise, you have lost nothing.
Oh, and with the volume control done in 24bit or better processing (it always is), you can reduce the volume 48dB and you still have a 16 bit resolution and still have a quantisation nose floor 94+ db down from your already very quiet signal.