Even if you are using SDH(not always available), you would still be missing things you could hear. Captioning is nowhere near accurate, nor complete enough to give you all the a movie presents.
Most of us STILL can't hear these things despite wearing HAs.
I understand. However, if you have it, my opinion is to use it. The screen and captions can't show everything.
For me, the music in movies(other than an actual song) is an annoying distraction. But, it is there to set the mood of the scene. I feel I'm OK without it, but I'm sure a hearing person would tell me I'm missing things.