A: No. The idea is that the Secret Cultist benefits from the end of the world in ways regular players do not, so everything is backwards — that which would normally make you lose now helps you win. So if victory is found through the Minions of Darkness, it’s just a bonus if Cthulhu himself also joins the party!
While the win conditions for the (non-secret) Cultist are more narrow, the same is true, since they’re winning with an UnGoal, reveling in the destruction of all we hold sane.