Yes, well, the selecting component has to be setImmediate(true) to make the ValueChangeListener call occur immediately when you change the value in the component. It’s hard to say much about your problem without seeing any code, but I’d first suspect some problem in the ValueChangeListener code and how it handles the choices.
I would be surprised if it there’s is some problem in toggling the invisibility as such, but you might have some type problem in handling the value - CheckBox value is boolean (or Boolean to be exact), as is the invisibility property.