You may get very few responses to this question, as many are against breeding, especially after recently watching the parrot confidential documentary. There are so many parrots in rescues and sanctuaries that many people feel very strongly against breeding more to just possibly end up in a rescue.
It sounds like you are a novice breeder seeking advice, so I don't mean to seem negative to this question, I am merely explaining why you may not get any responses that are positive to breeding at this time. Please go and watch parrot confidential, there is a thread here with links to watch the program, then decide if you still wish to breed.
I have not bred birds, but did foster some breeder pairs in the past. They were older birds and did not breed while in my care for a year. With that said, I couldn't tell you if you should or shouldn't offer a nest box. I think that is a personal decision on your part, as to whether you wish to encourage breeding of your pair or not. Good luck with whatever you decide, and welcome to the forum.
Have you handfed baby birds before ? Are you willing to sacrifice months of handfeeding around the clock ?