You won’t get a lower noise, because the 5V are generated from a switching boost or buck converter (depending on the number of battery cells)
To get a lower noise, the HAT or the USB DAC should be designed with a proper low-noise LDO and proper filtering to power the analog part of the circuit. The IC used as a DAC should also have good power supply ripple rejection, to avoid transferring most of the noise from the power supply to the audio output