Would he though, follow quizzy to world's end? (...) between his sense of duty to the people of Thedas, and his wanting to right so many wrongs if he has the power to do so, maybe he would apologize and part ways?
Hmmm... it depends on why the Inquisitor is going to the ends of the world. If it's for a selfish reason like personal gain or glory, I'm going to storm the Black City and take the power of the Maker for myself mwahahaha, I can see Cullen not following - but then I can also see such a relationship having ended long before the Inquisitor peaced out, too. If she was going for a "greater good" reason, such as... I don't know, maybe it turns out Solas wanted to rip the Fade open all along and it's going to tear the fabric of reality apart and destroy Thedas as we know it and the Inquisitor must go back into the Fade or go fight him at the ends of the world to save the people of Thedas from annihilation or whatever, then yeah, I can see definitely see Cullen not only following her, but being at the front of her line, ride or die.
Cullen is not that bound by duty, as we have learned, and as we discussed the other day, if he feels his duty belongs somewhere else now he will go and do that instead. He's not so stuck in his goal posts that they can't be moved forward. I can see, as the story progresses with a romanced Inquisitor, where the lines between his duty to the Inquisition and his duty to the Inquisitor cross and blur, become one and the same, and finally when the goal moves at the end. That hug in the ending scene, when the Inquisitor is back and he throws all protocol out the window because he's just so relieved to see her alive; to me it reads like his priorities have definitely shifted at that point. Certainly he is still loyal to the Inquisition in the end, he has a duty and a bond of honor with the people serving under him and the people who depend on the Inquisition, but at that point, if he doesn't even care anymore what such a public demonstration of the intensity of his love for the Inquisitor will tell their people, I think the Inquisitor herself has pushed everything else to second place in his mind. At that point? He would follow, yeah.
But then again this is all idle conjecture, because the reality is that, if we see the Inquisitor again in another game, she will most likely be alone. In my mind, Fenris and Sebastian would never have let my Hawkes cross the world throwing themselves into life-threatening danger on their own either, but that's just what happened, so... my romanticized headcanons aside, in canon Cullen would likely stay home doodling portraits of his soldiers, mending his socks and reading books with griffons in them while his Quizzie goes out and gets herself killed somewhere far, far away. 