No, they can only use the IP they've licensed. The licensing agreement is specific to certain characters and in some situations is actually geographically limited as to what characters can be used. From their annual report:
"In particular, our license agreements entitle us to use, subject to customary approval rights of Warner Bros. and, in limited circumstances, approval rights of certain third parties, all animated, cartoon and comic book characters that Warner Bros. and DC Comics have the right to license, including Batman, Superman, Bugs Bunny, Daffy Duck, Tweety Bird and Yosemite Sam, and include the right to sell merchandise using the characters. In addition, certain 9 Hanna-Barbera characters including Yogi Bear, Scooby-Doo and The Flintstones are available for our use at certain of our theme parks."
On a separate note, the Roald Dahl holds the licensing rights to that IP. Alton Towers closed their ride in 2015 when the Roald Dahl Foundation wouldn't renew the license.