"Some audiophiles claim that reversing the polarities of all the channels simultaneously makes a subtle perceptible difference in the reproduced sound
Yes I believe it can, I’ve heard the difference using dynamic speakers especially in the bass, but less so using planer,esl, types.
It’s sound it makes with dynamic speakers in that initial movement of the cone is out into the room (pushing) rather than backward (sucking), this pushing of the air on the eardrum has a more discernible sound rather than the sucking of the air, and gives a more leading edge to the start of the bass note.
Cheers George