Are they happy or not?
That may be a bit more complex. As Terril states, people are sometimes happy doing things that would make most of us quite unhappy. As Trouble says, though, they may be pretending- to others, to themselves.
Another possibility is that they are happy in a way, in accordance with the brainwashing they have received. Remember, they're living a lie. Staff and other dedicated culties do what they do because they are told they are saving the planet, "handling" their cases and all that. It's all lies, it's all bullshit. But they believe those lies. They believe the underlying premise. If they are doing what they set out to do- work toward something bigger and better- then that may make them happy despite the privation.
Now, take the same person, have him find out in some way that he's living a lie, that nothing he's doing helps anyone or anything, and make him do the same staff work. He's not going to be happy. There's no point to what he's doing; nothing to mitigate the privation and abuse.
When they go through his stuff while he's gone at post; when they tell him he can't leave; when they tell her that she has to have an abortion or that she has to leave her husband or never see her son or mom or friend again- this puts pain and sadness and duress into the equation. If the staff member starts wondering how the most ethical group on the planet and the people who are going to save everyone can't deal with a pregnancy or staff turnover or disagreement or just plain love between two people; the façade cracks and he's not gonna be happy. Enough cracks in the façade and he sees he's living a lie and that it's a cult. Those things that seemed to make him happy no longer will.
As brainwashing and conditioning fall away and the blinders come off and reality comes into focus, the person will discover that he would be truly happy living in the light of truth.