If the tame bird is under 4 about 6 months of age, it usually goes the other way and they copy the older birds and become wild so they should be kept apart until that age at least to cement the bond with people. Now, if the tame bird is already adult, and past the juvenile molt, they don't usually forget their trusting nature and can help tame other budgies.
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I put up two nest boxes on my budgie flock cage today. I have one bonded pair I really want some chicks from, both are recessive pieds so she is white with black and blue spots and he is yellow with green and black spots. They will have some gorgeous babies if they mate. My second female isn't bonded to any male, but it's better she have a box if she wants one anyway so she doesn't disrupt the other pair.
Makes sense, thank you!
Good luck with the bonding. Do you put anything inside the nest boxes?