I have pretty bad insomnia. My cage is in my room so all the birds have had to adjust to disruptions at night. I try to keep lights off so they can still sleep, but I'm often awake watching Netflix for hours trying to be tired. Regardless of volume, they never really seem to react. You'd be surprised how tiels can adjust to the environment around them. If you need music to sleep, go for it. If it worries you at all, I would play music and see how the bird personally reacts. If the room is dark, it's way more likely that they ignore the sounds around them to get some shut eye. I really wouldn't worry too much about headphones.