The answer is no because the Church has had interegnums lasting many years inbetween popes and the church has had numerous anti-popes.

The gates have not prevailed as the Holy Spirit is guiding and protecting the Church. These Vat II "Popes" make everyone think they must obey Vatican II. Ratzinger just sang the praises of Vatican II this week. But, it was not a council like Vatican I. It was more of and optional meeting of the minds (mindless) that put forth heresies that made uniformed persons think it carried the same weight as previous legetimate councils. But, the fact is that there is NOTHING binding upon Catholics that came out of Vatican II. And, the reason being they knew to invoke this would bring forth the wrath of the Holy Spirit. The Pontiff is prevented from teaching heresies when teaching faith and morals. So, they can pretend, and uninformed people can assume that they must obey Vatican II. However, as Catholics we must make it our personal duty to know the faith well enough that we can weed out rot like Vatican II and all of the many, many errors spewed since that time and toss them out.
We must also pray for all of the misled souls due to these "Robber Barons" leading people to hell. We must also, pray that those alive now see the truth.
We are close to the time when this will all be shown for what it is, and Christ's Church will be brought by him out of the mire that these heretics have pulled her into.

Yes, for example, the Pope resigned during the Great Schism, but from what I gather from this particular forum, sedevacantists accuse the Servant of God, Pope John Paul II of worshipping Satan and exhorting others to do so as well. If you believe that, then the gates of hell have prevailed against the Church.

sedevacantists aren't going to see it as "accusing" him - he accuses himself - it's just how it is, it isn't us determining that this is heresy and we now have the power of the papacy and we say he is outside of the Church - he puts himself outside of the Church by the very fact - and obviously what would be disputed would be whether what these "popes" have done actually constitutes heresy - considering that you are FSSP, you don't think that everything is all fine and dandy, or you do think that the novus ordo is a legitimate religion leading souls to heaven and the reason why you attend the traditional mass is b/c it feels more holy, it has that nice nostalgic feeling to it.  If you are going for the right reasons then you would have to admit that there is something fundamentally wrong with the Novus Ordo, and considering the responsibility for its promulgation and correction lies predominantly with the "pope" I don't really see how you can call him "the great" -other than in the most purely humanistic and modern philanthropic sense, but of course one could say the same for a whole slew of freemasons as well.

On another note, it bugs me when people act like discussing the issue of the papacy is too...extreme or not the real issue, or acting like sedevacantists are making too much of what really comes down to a matter of semantics.  I think that people have to try and be good Catholics, regardless of what they believe regarding the papacy, and that they have to try to always know the truth - that doesn't mean brushing issues relevant to our religion under the rug as something that "Christ wouldn't have worried about."  There isn't a dichotomy between spirituality and common sense - in fact the one is supposed to direct the other.  And Jesus was God Himself, He wasn't directed by a representative of Himself on earth, so of course He had all the clarity to see what needed to be done.  He also made a point to make it clear to the rest of the disciples that He was appointing a representative and that they were to follow his lead - Our Lord didn't have any intention of impressing on His followers that authority, especially the authority of the Church, was something to be disregarded.

trad 123 that last quote that you quoted was so, so sad - it's a good thing that everybody gets theirs considering how many souls they are giving full consent to to die in their false religion- tragic