I didn't say that it would happen. It is a hypothetical question to get Catholics to think about the true hierarchy of the Church and that in that hierarchy the Pope has no authority to go against Jesus and the deposit of faith. Although I don't believe that the scenario that I presented in the OP will happen, if it did happen I would realize that I was wrong and would change my view about it. However, even if it did happen it would not mean that the gates of Hell would prevail against the Church since the final victory will still be with the Church, not by what the Church can do for herself but by the intervention of Jesus when He returns and slays the Antichrist. Jesus said that the gates of Hell would not prevail against His Church, but he also said, "For false Christs and false prophets will arise and show great signs and wonders, so as to lead astray, if possible, even the elect." (
Matt 24:24) So it seems like there is at least a possibility for that scenario. And the Catechism of the Catholic Church says (added emphasis):
The Church's ultimate trial
675 Before Christ's second coming the Church must pass through a final trial that will shake the faith of many believers. The persecution that accompanies her pilgrimage on earth will unveil the "mystery of iniquity" in the form of a religious deception offering men an apparent solution to their problems at the price of apostasy from the truth. The supreme religious deception is that of the Antichrist, a pseudo-messianism by which man glorifies himself in place of God and of his Messiah come in the flesh.
676 The Antichrist's deception already begins to take shape in the world every time the claim is made to realize within history that messianic hope which can only be realized beyond history through the eschatological judgment. The Church has rejected even modified forms of this falsification of the kingdom to come under the name of millenarianism, especially the "intrinsically perverse" political form of a secular messianism.
677 The Church will enter the glory of the kingdom only through this final Passover, when she will follow her Lord in his death and Resurrection. The kingdom will be fulfilled, then, not by a historic triumph of the Church through a progressive ascendancy, but only by God's victory over the final unleashing of evil, which will cause his Bride to come down from heaven. God's triumph over the revolt of evil will take the form of the Last Judgment after the final cosmic upheaval of this passing world.
Notice that it says in the Catechism that the Church on earth will die just before Jesus returns.
So the question is: What kind of "death" will this be?
That's true unless the hypothetical situation in the OP were to happen.