The Last Rites: Do they guarantee Salvation?

Yes, on condition that the repentance was sincere. Anyone making a False confession - concealing the fact that he is not sorry and would do it all again – is not only not absolved, but has added another Mortal Sin to his baggage... but otherwise, yes. That is exactly what the Catholic Church is for... to get us poor sinners into Heaven.

NB with the Sacrament, we do not need Perfect contrition. Even the servile fear of Hell will suffice, because the Merits of the Passion of Christ will be applied and will suffice to 'fill up what is lacking' in our contrition.