If you mean production reds or that type... they will still breed with approximate qualities just not TRUE to their parent since they are crosses or they also won't be sex linked in future generations if you're talking sex linking. I understand genetics well enough to understand that. I don't consider sex link to be the best egg layers personally... though they do obviously put out a lot more eggs than some more dual purpose breeds. Biggest issues I see with production type birds is the excessive reproductive issues that set in after only a couple years reducing bird longevity and increasing heart break to keepers... who would even want to breed THAT forward?
If you're talking about breeding a high production bird like RIR, or Leghorn... those will breed just fine... regardless of which hatchery they came from.
Breeder birds aren't always easy to find... so I might use hatchery chicks... I just order a LOT of them and grow them all out, selecting only the best of the best and selling or eating the rest. With any hatching there is always extra cockerels... Are ya looking for MEAT production??
I've bred a lot of birds, I may not be grasping your question correctly but breeding for what YOU want... is always an adventure!