Honestly, unless a DNR oficer is also a falconer and is VERY meticulous in his feather ID, there is very little chance that he'll be able to determine the type of bird that your fletching came from. He'd probably be more concerned about the power of your bow or the effectiveness of stone points, not the origin of the feathers on your arrows.
I've seen bald eagle feathers that looked VERY similar to canada goose wing feathers.
As far as raptors being federally protected, I don't know a single person who shoots hawks. But I've seen dozens lying on the side of the road, killed by vehicles. The problem is that untold tens of thousands of different animals are slaughtered on america's roads, left only to rot or become a smeared stain in the asphalt. Deer, birds, squirrels, rabbits, raccoons, opossums, otters, beavers, foxes, bobcats, coyotes, ducks, hawks, owls, armadillos, housecats, dogs, kingsnakes, rattlesnakes, cornsnakes, copperheads, ratsnakes, etc..etc...etc.... ad infinitum die EVERY DAMN DAY by cars. That's a list of things I've seen on te road, and that's just off the top of my head.
If it's fresh and I can use its body parts for something, I pick it up. It's such a shame that animals pay with their lives because of our need to make the almighty dollar... a sad but true reality of the cost of our "advanced" society.