Does Billy Pilgrim find happiness in SH5?

Billy Pilgrim is a ridiculous character. From his silly toga, to his sparkly Cinderella boots, he is a ludicrously crafted idiot. But I wonder if he finds happiness? I believe Billy rejects reality because he cannot handle the terror and carnage of such a world. He accepts an ignorant bliss (Tralfamadore and time travel) as a new reality, instead of facing a grim world. I don't know if adopting Tralfamadorian philosophy make Billy happier, but I would argue that Tralfamadorian ideals bring him comfort. He makes peace with what he cannot change, but in doing so, he seems to absolve himself of all responsibility in his life. His attitude makes him life's plaything, even though he, by knowing the future, has the ability to change its outcome. It's ironic that Billy has the power to control his life, because he seems to surrender all control. Still, I think he makes peace with his life. He believes there is no difference between what he can and cannot change; he cannot control what happens in the world and in his life because all events are part of the unchangeable movement of time. The Tralfamadorians also seem to turn away when something displeases them. They simply close their eyes to avoid looking at whatever they dislike (Montana Wildhack screaming in the human zoo). Billy reacts in a similar (yet more complicated manor). What is accomplished by turning away from the bad and shutting out the unbearable?