Sleeping on an iPad 2 case is generally not a good idea, unless that iPad 2 case is the TyPillow. The TyPillow is a soft and cuddly iPad 2 case designed to double as a pillow.
The TyPillow measures 17 inches and has a small felt carrying square designed specifically for the iPad 2. The pillow is designed to let you use your tablet with ease no matter where you are. Perhaps the biggest advantage of the TyPillow, besides the ability to take random naps with it, is that it can effectively absorb nearly all of the heat generated from intense tablet use. If you want to see the TyPillow in action you can check out the video and pictures here. In case you're curious, the TyPillow sells for $35.