I have the same worry. I have 11 cats and two dogs. The cats have their own room where the dogs aren't supposed to go unless invited. Some of the cats come out to visit and some never do. They have a cat pen, but one of the cats never goes out either. The dogs won't harm the cats, but the cats aren't too sure of this. I close the door to their room when I leave the house and open it when I can supervise. The poor cats don't get much of my attention so I wonder if they're happy.

As long as Brody isn't showing any signs of being miserable (extreme lethargy, inappropriate peeing), I would guess he is as happy as he can be. Cats are very accepting of life as it is rather than what they might be missing. We should be more like them.