I’m not a game bird biologist, but I doubt of many or any pen raised birds survive very long in the wild.
I worked on a bobwhite quail radio tracking project and the wild birds didn't do too well either. Weather and habitat play a huge factor as well as predators. It's interesting that pheasants, chukars, and gray partridge were all successfully introduced a 100+ years ago but we can't keep the populations going today. Habitat and predator control(especially) are things that aren't being addressed.
I expect to see more pen raised bird hunting in the future as the human population continues to grow.