Let's make this more simple - a female parrot can and usually does lay eggs on her own if no male is around.
If there is no male, she usually will eat the infertile eggs after a few days.
If she lays eggs and there is a male in the tank at the time she lays, and he is the right species to fertilize the eggs, and he actually pairs up with her and squirts his jizz on the eggs as they are laid, then you might have babies a week later.
If you keep her in the tank with the rams the eggs will never do anything.