I'm not sure cooked chicken will do them any good but fill a space in their guts. Their digestive system isn't geared for metabolizing terrestrial animal fats and oils. And any supplemental hormonal, amino acid, and mineral benefit is bottomed out from the cooking process. I'd also have some concerns about what the chicken may have been treated with before slaughter (antibiotics, hormones, etc.).
The chicken may yield zero adverse effects. But, any potential issues, to me, is not worth the risk to my collection/investment.