I did this intentionally in a dream a couple months ago.
Spoiler for the dream:

I was lucid, but it wasn't a song I've ever heard before outside of the dream. Oh! and once I started the music playing, it kept playing for the entire duration of the dream.
Usually when songs start playing in my dreams they are spontaneous though. I can only seem to remember hearing songs from waking life in dreams when I'm non lucid.

Something that I've noticed lately is that whenever I'm falling asleep, my dreams will almost always start with a song playing in the background. I have experimented with it on a couple of separate occasions now. I wait until I'm starting to see a dream and some song will almost always start playing, then I will wake myself up and wait until another one starts. I repeated that several times to see if it was a new song each time and it was. They're completely original songs as well, I think it's really neat.
I have been thinking about writing some of them down, because I can remember them really well for some reason (something that's unusual for me, because I always have a really hard time remembering the songs that I play or hear in dreams once I wake up).