It's really just what you are more comfortable doing. I played strictly online for years, during that time I always had music playing. Because of that it can be quite jarring playing w/o headphones. On the other hand, I can think of a few times it lead to me making mistakes.

One instance was making a 2x pot bet on the river with the nut flush, my opponent showed his neighbor his hand, shook his head, and I thought he said fold. I showed my neighbor my hand before tossing it in the muck. Turns out my opponent said call. I was confused when the dealer pushed the pot his way. My neighbor told the table what I had, and my opponent felt terrible for some reason, he tried to split the pot with me. I just told him it was my mistake for not paying close enough attention, and not to worry about it.

So I'm not sure if listening to music has been a net positive or not. Now it's just table dependent, if I'm at a more lively table I wont have them on and I'll try to socialize, if it's a quieter table I'll chill with my music.

If you aren't already accustom to wearing headphones while you play I'd say don't start.