I do not think the CVN is viable against an enemy for whom it poses an existential threat.
I know most don’t agree, and, obviously, we won’t find out until the shooting starts.
People that don't like CVNs speak of them as floating in the middle of the shooting, all alone. Couldn't be any further from the truth. Some say CVNs have not been tested in a close-in shooting match. By design, of course not. They project power from a distance while being defended by formidable air, surface and subsurface assets.
As for their “viability”, in the last 40 years there has hardly been major military action anywhere on the planet that has not included a CVN. There are a lot of US presidents that would attest to their viability. Not many foreign terrorists and dictators though, since many of them are dead.