Can POP (Plaster of Paris) and Paint done without waiting
POP (plaster of paris) achieves full hardness in about 12 days at STP.  but for your purposes its entirely cosmetic.  you should be able to very safely paint 24 hrs after installation.  give it an extra 24hrs on the ceilings to be safe.  you can help things along enormously by using a dehumidifier to speed up the curing process