True.
To go into a bit more depth here, one of the features of Mickey Mouse is that, compared to the other characters, he is rather large for a mouse. So if Looney Tunes have a "Mugsy Mouse" character, he's unlikely to be as big as Bugs Bunny. That changes his interaction with other characters, for example he won't be competing on equal terms with Daffy Duck or disguising himself as a woman to fool Elmer Fudd. He'll be more like Speedy Gonzales than Bugs Bunny.