No Calamity, but I feel the Final Days repeating is pretty much worse than any calamity could be. So we don't need a calamity, when narratively, the literal fabric of reality is being torn to shreds by the end of the world.
We'll likely see this represented through custom weather; which they already did on the First, as well as client side changes like they did with Rhalgr's Reach at the start of Stormblood and do with the Beast Tribe areas. There's plenty of ways to mess up the world on a client-by-client basis without ruining the game world for everyone playing—they've been experimenting with this more and more of late; think of how Puppet's Bunker's quest blew up a literal mountain range to reveal it for those on the quest.
So we can expect things like that I feel.