Um… No. your body is hospitalized and in a deep coma, but the coma isn’t where it’s hospitalized. Add a comma after hospitalized to fix this.
Capitalize Earth. (Guideline: if you can replace it with world, Earth should be capitalized, but if you can replace it with ground or soil, don’t capitalize it.)
Get rid of the dash after asleep and replace it with a comma. Although the sentence is not compound, you still need a comma after asleep for clarity; otherwise, it could sound as if you’re saying the possessed person, after falling asleep, decides to deliver justice to the world.
Your body is hospitalized, in a deep coma, but your soul is free to wander the Earth. You have discovered that you can possess people until they/you fall asleep, and have decided to deliver justice to a world in need.
For the record, possessing people’s bodies without their knowledge and consent isn’t just, as a general rule.