[armydoc]

Jesus gave authority to continue spreading the Gospel to His Apostles. The Apostles appointed successors, bishops, to continue the mission. There are only 2 branches that have valid apostolic succession: Catholicism and Orthodoxy.

So the Orthodox maintain "valid" apostolic succession without obtaining salvation themselves?

"We declare, say, define, and pronounce that it is absolutely necessary for the salvation of every human creature to be subject to the Roman Pontiff." Pope Boniface VIII in his Bull Unam Sanctam issued in 1302

"Where the necessity of salvation is concerned all the faithful of Christ must be subject to the Roman Pontiff, as we are taught by Holy Scripture, the testimony of the holy fathers, and by that constitution of our predecessor of happy memory, Boniface VIII, which begins Unam Sanctam." Pope Leo X, Fifth Lateran Council (1512-1517)

[dangus]

Putting aside your quotes out of context, yes, it is possible to be in apostolic succession without attaining salvation of yourself. The sacraments do not rely apon the sanctity of the person who validly performs them, but rather on the grace of God alone.