That depends on Twentieth Century Fox. Usually any item from a contract agreement with another film company or licensed property has a rule that requires it to be destroyed or not visible to the public if the original agreement ends (i.e., the attraction the agreement was made for closes).
I could see generic props like boxes, plants, and the even the gangster car transported to other parts of the park or other attractions, but anything that can easily be traced (the flowers or munchkins in Oz, the Arc of the Covenant, the spacesuits and Aliens from Alien) will be torn apart.
Although now that I think of it, do you think the Arc of the Covenant in the display cases was simply a mold of the one in the ride? or the actual thing from the movie?
Sometimes fabrications are passed off as the real thing..it happens.