Unlikely to be succesful. The powder burns on the surface. Making a single lump reduces the surface. Would be like setting fire to a folded newspaper compared to setting fire to the individual pages crumpled up. It might burn, but will take much longer. I think you will find the single piece charges made comercialy will either have a porous spongy nature, or more likely will have additional chemicals to control the burn rate. Where single pieces are usefull is in things like rocket motors, where the burn is up a central hole, and as the powder burns the hole gets bigger, giving progressively more surface and afaster burn.
I also think you will find ping pong balls are not cellulose. They may be nitro-cellulose, but if so this is chemicaly similar to smokeless powder or some explosives, and it may not be a good idea to add such material to a blackpowder gun.