Not all ‘popcorn ceilings’ contain asbestos. Most all of it is simply a finishing compound, and there are many ways to finish it, ‘popcorn ‘ or ‘dabbed’, or other textured ceiling.
That said, I do agree with skim coating over it if a smooth texture is preferred. I’ve had that done quite a few times in my clients homes over the years. The texturing was simply preferred by many builders to hide potential ‘nail pops’ and not have to be included in any warranty work. So, textured ceilings were used a lot. I dislike them.
In terms of acoustical treatment for the OP, not sure you need to do it for that reason. You may want to purchase a box of 24x48 ‘reflected ceiling’ tiles used in ‘drop down’ ceilings, temporarily attach to the ceiling and see if there is any benefit before going that route. If so, you can get ‘acoustic’ (not in the audiophile sense) 12x12 ceiling tiles that can be interlocked and applied to the ceiling. But, my personal preference would be a smooth ceiling, and then possible true acoustical/diffusion panels attached where/if needed.
You don’t want to make the room too dead.