You can take a tube but they may not let you use it in the lazy river area of SAB.
DD7 always takes a tube with her and we've never had a problem - they even sell children's tubes at the hotel. She doesn't use it in the lazy river part though as that area is very deep, especially for children. It's not like the lazy river at TL or BB where you can stand up and touch bottom. DD18 and her friends occassionally rent a tube but honestly, it sits on the side most of the time. Noodles are inexpensive and work just as well for us.
You could always buy your tubes and take them along but ask first before opening them for an "official" ruling. That way, if you couldn't use them you could return them with the receipt when you got home for a refund.