So I ran a mission and rescued Bottle & Cappy. They now show up randomly, and I've seen some people's happiness rise, one in particular went from 10% to 75%.
Now one of my quest runners (basically my Avatar in the game, so I keep a close eye on him). He recently died, and on revival, his happiness has dropped to 10%. Now, since he's one of my primary quest runner, he doesn't get assigned to a room.
So will Bottle & Cappy cheer him up while he's wandering around the vault?