I generally don't listen to music while I read, but that's usually because of situation/environment. I generally read in the canteen on my lunch break, on train journeys (can't read on a bus - makes me sick), or last thing at night in bed.
I do listen to stuff while drawing, but it's so rare that I draw. My efforts lately (design for my sister, a birthday card, Bert Shakespeare, and the advent calendar thingy) is probably the most I've drawn in one block for decades. I'm really out of practice. I listened to two podcasts while I drew recently, which is something I almost never do. I don't usually have time to listen to podcasts, but found drawing recently was just that perfect moment.