for an audio signal within the rails of an opamp, can its quality be improved by the + and - rail voltages?
In general, you want your input signal to swing close to the rails of the ADC’s specified input voltage range, in order to maximize the converter’s dynamic range.

Make sure you back off a little to accommodate any gain error of the device.

From TI doc SBAA004A


  The signal amplitude should be closely matched to the analog input range of the A/D. This is done to maximize the dynamic range of the converter. For example, if a 12-bit converter with a 20-V input range is selected, the value of one LSB is 4.88 mV. It would be ineffective to use only a small part of that range, for example, if the input signal was 2 V. A better solution would be to select a converter with a more optimal input range, or to insert a gain block in front of the A/D (keep in mind new errors which the gain block will introduce). Many high speed converters, due to process voltage breakdown limitations, have small input ranges. If the signal bandwidth is small and a high degree of accuracy is needed, it may be advantageous to consider using a lower speed A/D with a larger input range.


edit per comments:
The voltage level of the rails to the op-amp won’t have any affect on noise, so long as it’s   in spec and the amp stays thermally cool and regulated.