This doesn't work because, as you said, org-mode uses its own keybinding for C-TAB. In other words, even if you define a global keybinding, as soon as you invoke org-mode, it will overwrite that binding with its local keybindings.
What you can do, however, is add a callback function that is invoked whenever you start org-mode, and in that callback function you reset C-TAB to invoke switch-view:
(add-hook 'org-mode-hook (lambda () (local-set-key [(control tab)] 'switch-view)))
Put the above line in your .emacs file and next time you start a new Emacs you should be good to go.