I went with "No" on this one. I don't thing modern day popular music belongs in a Medieval RPG, or even most modern RPGs.
Further, you have to take into account different musical tastes. Personally, I don't really care for Jimmy Eat World, and including them in any game, especially an RPG, isn't a huge selling point in my book. On the other hand, I love Green Day more than pretty much anyone, and I still wouldn't want to see them in a Medieval RPG. So I say no, stick to Medieval-type music (or even some game tracks) or just use the default stuff.