If the Russians were serious about sinking a carrier, then they would use a nuclear warhead, not conventional ... and that would take out a carrier.
In fact, any skipper, worth the name, would assume that in such a situation that any missiles coming against his ship would be nuclear and act accordingly.
There is no real defense against a nuclear warhead blowing up within a few hundred yards of a ship. That said there will never be another nuclear war if both sides have them. The last 70 years have proven that. Hell, we didn’t nuke Korea or Vietnam and there wasn’t threat of retaliation.