The Priest questline is simply an alternative to running C'Thun as a tool against control mirrors. C'Thun is generally bad (outside of said control mirrors) as it dilutes your deck with 4 mediocre/bad cards. The questline forces you to run some 5- and 8-drops that you normally also wouldn't, again making your deck slightly worse. It also makes your mulligan worse in matchups where you don't care about finishing it. They are both very slow. The main advantage of the questline is that it is more reliable than C'Thun in those control mirrors (in terms of killing the opponent).
However: it's not an auto-win vs control decks. Other control decks can run disruption cards, their own OTK-type win conditions, etc...it will only be an auto-win vs ultra-greedy, sub-optimal, 'fun' decks.