[gr8fl4porsche]

Hard to tell with that pic but it looks to me like thinned down joint compound sprayed on the ceiling and rolled with a paint roller.

Adding a layer of drywall will be a lot of work.
Making it smooth will be a lot of work.

Try a closet or something small.
Sand or scrape off as much texture as you can.
Apply 2 skim coats.
Sand and paint
Let us know how it turns out.

I skim coated every surface of my house during a recent remodel. I try to get the walls and ceils as smooth as possible. Texture bugs me. Its a cheap way of finishing that is meant to hide imperfections and save cash.