If someone breaks into my house, the last thing I'd be worried about is whether or not they are a local or not. Why would it matter if the species was native or not, if it's harming your chickens? Besides, as has been stated here before, you cannot eradicate a species by shooting them. For every one you shoot, a dozen more will take its place. It's true! I read it here on BYC. It does amuse me that this principle seems to only apply to certain specie, such as coon, possom, etc. No one buys this baloney when it comes to species they perceive to be endangered.
Species are placed on the endangered, protected, or threatened list because their numbers are low, their reproduction is inadequate, and the threat they face from predation and loss of habitat is too high to overcome. They are not assigned endangered, protected, or threatened status by backyard joe blows who "perceive" them to be endangered. You might want to check out the U.S. Fish and Wildlife Endangered Species Program web page for more information:
http://www.fws.gov/endangered/
No, you are not likely to eradicate your entire local popultion of raccoons, or opossums, because they reproduce like wild fire, habitat is very easy to come by for the most part, their resources are abundant, and their natural predators are generally lacking. If you shoot 10 opossums on your property, you simply open up more habitat and resources for 10 more to move in from neighboring farm lands. But species that are much less abundant and not as densely populated CAN be more easily controlled through eradication. But shooting only one Fisher Cat on your property means that you might not EVER see another one again because their numbers may be very low (depending on where you live). Where I live, I have seen one Fisher and accoridng to my state's DNR, Fishers are not terribly common. But I have seen hundreds of coons and opossums over the years.
In my state, an example of this would be the Canda Lynx, the Whooping Crane, the Timberwolf. These species were hunted or poisioned to near extinction but have made a comeback due to protection. The wolf's habitat for example, has shrunk every year due to urban sprawl and industrialization. People began hunting and trapping them without mercy because they were feeding on livestock. Calves, lambs, chickens, even foals and domestic dogs became food. The rate that they were hunted and killed overcame the rate they could reproduce and rear young. With the loss of habitat, the loss of food, and the intense predation from humans, the species was almost totally eradicated. The DNR planted packs of captive bred wolves in this state to re-establish the populations.
But for all of the trapping and hunting of coons, why aren't they near extinction? Their numbers just keep growing, despite the very healthy and active population of coon hunters raising coon dogs around here. Coons can reproduce so fast, and so efficient, that hunters cannot overcome their numbers. In fact, for species that reproduce and rear young very efficiently, hunting is an EXCELLENT way to guarantee a healthy, reproducing population. By thinning out the herd, you open up more resources (land, food, and breeding opportunities) for the remaining population (deer and rabbits also come to mind.)
So yes, my opinion still stands that shooting 10 or 20 coons a year that are threatening your free range chickens is absolutely NOT an effective way to control the poulation. If anything, you are only strengthening the population by opening up more food and habitat for others to move in. Not only do I believe this because of published research and results, but also from my years of watching my grandparents hunt and trap chicken predators continuously and NEVER making any dent in the population, whatsoever. They raised all types of fowl for meat and egg production and I don't ever remember a day without some type of predator hunt. Most of the pens were not secure (chicken wire) and could be ripped into. Many of the birds free ranged. Some of the guinneas and peacocks even roosted in the trees. The ducks would wander over the hill to the pond and get eaten by snapping turtles and fox. The constant killing just never made a single bit of difference.
I think you need to remove habitat and food sources (e.g., lock up grain bins securely, keep chickens in SECURE pens and runs, thin out underbrush and excess vegetation that provides hiding spots, remove breeding habitats, keep property clean and well inspected, keep up on mowing and brush hogging, trim low hanging branches, etc.) But constant shooting and trapping as the main source of protection is ineffective for the most common chicken predators.