No, it does volume control digitally - lower volumes *will* loose resolution. It does dithering, etc, internally. This, as you say, is very common in highly integrated digital audio solutions. There is a curve on the SAA7705H specsheet which shows the THD+N curve vs volume setting (page 15 on mine).

Note also that the DACs are 18-bit (and the internal path is 18 bits wide), which gives us 2 bits of attenuation (6dB) without any loss of resolution. You'd be looking at a very low noise external attenuator (eg, LM1972 as used in the Rio Receiver) with good PCB layout to give an analogue volume control with less ill effects than the existing digital one.

Some DACs, eg the PCM1716 in the Rio Central/Rio Receiver, are 24 bit, allowing 8 bits of attenuation without loss of resolution on a 16-bit signal.

Hugo