Oh my. Let's pretend for your sake you didn't ask that question here since capturing wildlife without a permit is highly illegal. Scavenging nests for eggs is also illegal. Even if the nest would be destroyed during construction or some such thing you aren't supposed to touch it at all.
Fish and game departments also learned that quail once captured will often waste and die when moved to a new location. This is a common happening though, many wild born animals will die if caged.
Releasing bobwhites without a permit is also highly illegal. Every state in the US requires a permit to raise bobs and further permitting to release them. Diseases like coryza, MG, and blackhead could be devastating to what local birds you have left and none of those diseases can be tested for or treated in quail. It is much better if caged birds are only released with the intention to collect them all such as a game bird shooting farm.
Further, restocking has proven for nearly 100 years to be completely ineffective. Restocked birds don't have the capacity to brood or raise young or evade predators. Hold over release birds surviving are common but in no way desirable genetically. Your birds breeding with wild stock would be a shame since they possess such diluted genetics. No matter how wild they seem in the flight pen they are domestic bobs and domestic bobs aren't wild bobs.
The real key to restoring a population is giving back their habitat. Brush piles and other hiding places as well as planting things they can reach to eat. They aren't going to jump to knock down the not always native "hay" grasses that grow across most of the nation. People removed their habitat and food sources which is why you don't see that many quail. Releasing more quail into an inadequate habitat with inadequate food is never going to solve the population problem with bobs in the Southern states. Generations of large scale farming made the bed that we all have to sleep in. Until you change the landscape you won't change the quail population.
http://www.noble.org/ag/wildlife/stockingbobwhite/
http://www.wildlandforestry.com/Pages/bobwhite.aspx
http://mdc.mo.gov/blogs/more-quail/why-we-dont-stock-quail