Well, Dagon is supposed to destroy Existence. Towers are being "nullified." The world IS technically screwed by the mere fact it exists.
Destruction of the Towers would destabilize existence, for they harvest Creatia to keep existence going. After all of the others get obliterated, the last, I'd imagine, would be the Ur Stone/Tower, Direnni, which I don't necessarily know how that would happen. We also can't forget the existence of the Wheel within the Wheel, White Gold, and the 8 towers around it; such a mythic structure would have undoubtedly bad effects if the Ayleids did whatever they intended to do with them.
All this said, I'm confident the Dawn would return; destroying the "anchor of all existence" would undoubtedly have bad effects for the Aurbis. Recall that Alduin is essentially Anu and Padhome combined and can kinda be seen as a looming force rather than an entity with a direct impact on Nir, like perhaps a Daedric Lord has.
In the end, this is all my opinion though.
edit: Sorry I screwed a name up.