No one else is likely to notice the difference, but you. Maybe someone who was present at the performance, maybe.
By experiencing the live performance in person I tend to internalize the "correct" L/R channel assignment. Then when listening back later its interesting to flip L/R back and forth. Often one way sounds correct and the other often sounds somehow wrong, and that's sometimes not subtle. Other times it really doesn't seem to matter. I think this is because I'm really listening critically and comparing against the memory of what I heard live. I doubt casual listeners who were at the event will notice, unless there was something rather obvious differentiating left from right. Folks who weren't there and have no a priori idea of how the stage was set up or what occurred during the performance won't notice.
You can flip Left/Right at any point in the signal chain- at the mics, cables, recorder, in the DAW, by splitting and recombining the stereo WAV, anywhere in the playback signal chain, and the end result is the same. With headphones its super easy, and makes for a good check of balance. When mixing more than two channels it more complicated since each individual pair then needs to have the correct assignment relative to the others. Need to make sure all Lefts are routed left and all Rights routed right, but after that can flip the mix back and forth as you like as before.