Well we should try... but I always try to avoid operating devices powered by lithium batteries in low battery and high absorption conditions.
There are technical reasons for this.
When lithium batteries are close to being completely discharged, they tend to increase their internal resistance, and this leads to greater power dissipation inside them (they heat up).
At the same time, the device's power supply (DC/DC converter) tries to continue to maintain its constant output power, but having the lower input voltage, this translates into a higher input current (absorbed by the batteries), which therefore they are in the worst conditions:
they have to deliver a greater current than when they were charged, they have a greater internal resistance, and therefore heat up more.
To answer your question, making a hypothesis (having never tried), if the device has an excellent internal DC/DC power supply, the sound quality should be affected little, because the power supply tries to keep the output power constant .
Likely, no matter how good the power supply is, it may have difficulty performing its job well, especially during fast musical transients, which translate into transients of power absorption from the power supply.
So, yes, the sound performance could in my opinion be negatively affected.