On their own the parks probably would survive a severe depression unharmed (Disney's mismanagement of the parks is exponentially doing more harm than any outside influence could possibly do), but I doubt any other portionof the company would survive in one piece. Disney's film and television library would defnitiely survive (except for the terrible excuses for movies that Disney has released the past several years), ESPN could, and maybe some aspects of the consumer products division would survive, but everything else would self-destruct and get sold off in pieces (but that it already happening). The sad part is that all of Disney could be morphed into a juggernaut of a company that everybody else could not stand to compete against, but Eisner and his cronies have pretty much tore these assets apart. If a CEO with a vision and a large amount of pride would step in RIGHT NOW and turn things around, Disney will have no problems surviving whatever is thrown at it. However, with Eisner (and by extension the big time idiots that he has promoted during his reign) continuing to run Disney into the ground at a horrifying pace, in 5 or 6 months not even a "Dream CEO" could salvage Disney as it is now.
The bottom line is that if the economy were to take a nosedive, Disney as we know it would cease to exist immediately. Then again, Disney as we know it will cease to exist in the not-to-distant future, so maybe this talk really doesn't matter...