Cool idea, but we arn't limited to only death sounds, every sound in StarCrafts MPQ's (weapon sounds, deaths, voices, etc.) can be used in a map with 0 increase to file size! I think it would be hard to make a song that wasn't annoying, but there are lots of sounds to work with. If it was done right I think it could work well.
Depends on how you define music. Some say it's a replicable order of sounds in time. Some say it has to be pleasing to the ear. (or their ear(s), in particular) Some say it requires instruments. (the voice being one)
So, can you? I would say yes. Doesn't mean everyone will agree.
A few years back, I had this idea too. I was going to make a Christmas themed movie map were the dying units made bad representation of the song jiggle bells.
There was a lot of math involved, and it was way too time consuming. I eventually scrapped it.