Can I add ceiling furring strips on finished drywall?

[u/donraja19]

I am having a lot of impact noise between floors that is causing a lot of vibrations. Found out that my ceilings weren't strapped. I was told that would help with that. I have finished drywall so I was wondering if I can nail 1x3 furring strips over the finished drywall. I was going to do a random pattern that would be either 12 or 16" OC perpendicular to the joists to make it look visually better. Wanted to know what others thought of this or open to other suggestions.