Hi, Jamie! Yep, I've taken an eight-year-old daughter with a broken left arm to Walt Disney World Resort. When they put on her cast, we paid the extra to get the waterproof one. The broken arm didn't stop her at all. If your son doesn't already have a waterproof cast, I would check into getting one for him. There are more water rides and play places to get wet than you might think. You also need to take into consideration ease of showering, the pools, and/or water parks.
There is one thing to be aware of, though, that disappointed my daughter. The characters are not allowed to sign anything (casts, t-shirts, etc...) on a Guest's body. She had hoped they could sign her cast, but they are not allowed to do so. Prepare your son for this so he won't be disappointed.
Some Cast Members commented on her cast and asked her what happened, several gave her stickers, she was, literally, sprinkled with pixie dust, and once given front-of-the-line privileges. Cast Members at Walt Disney World make Magic happen everyday. You never know what they might do. Sorry about your son's arm, but don't let it hinder your fun. Have a Magical vacation!