Yes at 20 years old a Caique is past prime breeding age and by this I mean it would be far too hard on its system to raise babies, care for young and raise to weaning. Appropriate age would be 2-10 years old. Past that age is gets too hard on their bodies with so much nutrients going to chicks, incubating and energy feeding them.
That being said, they can mate and there's no stopping that behavior, but breeding would not be recommended for such an old bird. At this age its past its prime, possibly infertible and would likely exert much energy in having to raise chicks.
If you are intending to breed a 20 year old caique, I wouldn't recommend it at all.