Prevent noise? Not from your neighbors. The popcorn may allow for a slight sound diffusion (not absorption), but it isn't going to help with sound transmission from above. It's usually sprayed on concrete ceilings. Not sure of your construction type, but if you live in a high rise, you may be exposing concrete if you remove it.

Do you have room to install a faux ceiling with sound proofing?

popcorn ceiling doesn't do anything for soundproofing.
it's a dirt and dust catcher.
what would help absorb noise from neighbors would be insulation in the ceiling, or a second layer of drywall.

removing popcorn ceiling is messy, but easy as pie.
use a garden sprayer and water.
make sure you have plastic drop cloths on EVERYTHING.
spray the water on a section, let it sit for a few minutes (2 or 3), then scrape off with a wide putty knife.

once it's all down, give the ceiling a light sanding, then paint it as you like.

My ceiling is low 8 feet I think. What to add to reduce step sound from above? Sounds like removing popcorn is better than leaving it there.

Were houses built in 1997 in Florida done with popcorn ceiling?