It still has ghosts and souls in it, in a universe that never dealt with that sort of thing, for various good reasons.
Darkmatter still exists in our dimensions, otherwise it wouldn't really affect our universe. So in reality, it's part of our universe and our dimensions.
The underworld itself you claim to not be a physical thing. Therefore it cannot be made of Darkmatter, which is a physical thing.
This essentially leaves the existence of such a thing up for debate, which the community is very entitled to decide upon.
You are also proposing that a soul is made of darkmatter, which defies scientific measurements (Simply weigh someone, then weigh their body parts individually, usually once they die).
Your proposal also says that each person, with their soul, dying causes it to increase the amount of darkmatter. This means that the non-darkmatter mass of the universe will slowly run out till there is only darkmatter. No mass or energy can be destroyed or created remember, only transfered from one form to another.
Which again doesn't entirely make sense.
This is a good piece of roleplay by a character ingame maybe but it isn't how I, nor others, view the Discovery universe and I doubt it will ever become accepted as canon.