No score or soundtrack?
Yes. I haven't seen it a few years but when I watched it for the first time on DVD I rewatched it in its entirety just to see if I was right in thinking it didn't have any music.
The only thing I remember was a light, building-intensity droning sound when Tommy Lee Jones' character visits the motel at night to inspect the Llewelyn crime scene.
They could have purchased the "music" for the entire movie for $3 off of any royalty free music site...unless there are period ambient radio music sounds somewhere in the movie that they had to buy the rights to.