Can Catholicism exist without the church?

This is a thought experiment, more than anything.

The other day I was thinking about how during the Cold War, the world feared a nuclear holocaust which would wipe out the globe. Of course, this wouldn't be realistic. A nuclear exchange would likely devastate the northern hemisphere, but civilised society would endure and recover. Meanwhile, the southern hemisphere would be relatively unscathed.

Nevermind this, say a worst case scenario does happen, and some apocalyptic event wipes out national governments, transport infrastructure, communication networks, etc. Suddenly, Rome (if it hasn't been flattened) cannot communicate with, say, the Archdiocese of Buenos Aires.

Christianity will endure, no doubt: Local parishes will stand, and bibles will remain. But I predict that over time, as the different Catholic communities must find their own ways to adapt, they'll diverge, no different to how the Orthodox and the Protestants once did. And without communication, the Church will lose its ability to enforce communion. So, after a hundred years, who will be Catholic? Will Catholicism even exist, or will it be extinct and there'll simply be a large number of Catholic-deriving denominations?

The Holy Spirit is meant to protect the fundamental truth of the gospel, no matter how corrupt the world becomes. But schisms have happened before. Is there any theological or ecclesiological rationale indicating Catholicism as we conceptually understand would continue to exist?