Graco doesn't recommend it. They say just to use a damp cloth or sponge with hand soap or dish soap. Stay away from harsh household cleaners, and never use bleach to clean your Pack n' Play.
I think one concern is that parts (like this) that aren't designed to be submersed in water tend to have a hard time drying out, and since they remain damp inside, it can promote mold, mildew, etc, and you don't want your baby sleeping on that. Unfortunately, the best mold remover is bleach, which is way to harsh of a chemical to use on a Pack n' Play.
My advice is to try their recommendations (damp cloth or sponge + mild soap) and if that can't get it suitably clean, then to order a replacement matress/padded base. It's cheaper than buying a whole new Pack n' Play. Graco sells replacement parts on their website here, just enter the model number and serial number to select the correct part:
Or if you have any trouble with their online order form, you can call them at:
800-345-4109 (US - 8am to 5pm EST)
800-667-8184 (Canada - 8:30am to 5pm EST)
I hope this is helpful. Good luck!