you can, but it substantially increases the "fun" factor. Its one of those things I'd do just to prove it can be done, not how I'd recommend doing it.
depending on why you want to remove the shroud its easier to remove the fan, the only reason I wouldnt pull the fan to do it is if I was pulling the shroud to replace the radiator only. Then I'd unseat it to allow the radiator to be pulled, the only justification for doing it that way is that you dont care if you damage the radiator on the way out.

