Radiosity is really for realistic setups. Ever watched Fight Club? All the CG in that was done using radiosity renders. Looks great, but takes an immense amount of time to render out.
Cartoons usually don’t require such detail. I don’t think even Pixar and the Dreamworks CG group (PDI?) use radiosity in their movies. The point of radiosity is to fool the eye into believing an object is actually there – all objects reflect at least a minute amount of light and color, affecting the objects around them. The mouse in your hand is actually a different color than it would be by itself under the same light. Toon shaders go the opposite direction – they remove color detail, usually producing smooth banding.
If you want real backgrounds, tho, you could do a single radiosity render of a set and then composite characters over top. Kills off creative camerawork, though.