It depends on what kind of curve the volume control uses but assuming 50% volume is half the amplitude (-6dB) you will only lose 1-bit of resolution. To lose half the bit depth you'd have to turn it down by 48dB!
It's worth noting that perceptually, half the volume is actually closer to 3dB (a halving of energy), which is only half a bit of loss.
If a floating point audio pipeline correctly dithers the signal going into the DAC it's unlikely anybody will notice any quality loss by using a digital volume control (even at 16-bit). You might hear the hiss of the dithering if you turn up the analogue portion of the chain, although you'd have to turn it up quite a lot.