It really depends. I know at least one game that has done it for a few areas off the top of my head: the undersea palace in Chrono Trigger. I think the things to consider are:
- Your battles should happen on the dungeon map, without a screen change. Else it might feel weird and unintuitive.
- Doing this might be more immersive dungeon wide but will create a more drawn-out feeling for your dungeons. Sometimes, in particularly intense locations, you might want this, but sometimes you also like your dungeons to have a little breathing room, give your players a bit of a break.
- Battles are intense, they're mini climaxes. If you are going to do this, your dungeon theme is going to have to reflect that at least partly. It will have to be at least somewhat energetic and driving. Sometimes you might want a dungeon to feel empty, desolate, sad, whatever. Such a music would likely not create much hype during a battle scene. I mean, having a battle scene with a sadder song can totally be an option to create an effect if the context and story supports it, but would you want this for just any regular battle throughout a whole dungeon? Battles are already a bit of an hindrance, a necessarily evil, imagine if it was not somewhat driving on top of that!...
So bottom line I think it's definitely a tool you can use in places to create an effect. It works for the Undersea Palace in CT because the theme is driving and it happens near the end of the plotline when you are about to confront (what you think is) the main bad guy. But game wide it would have to be a very intense and driving game for it to be appropriate. I dunno, I guess it could work, but I'm not convinced.