This would be an interesting test case for state and municipal level registration. Way back in 1968, the Supreme Court said in United States vs. Haynes that the NFA violated a man's right against self-incrimination (5A) by prosecuting him for failing to register an illegally possessed firearm. He was a convicted felon, prohibited person, so registering would require incriminating himself. They had to amend the registration requirement to only apply to those who may lawfully own a firearm. But the original Haynes decision basically bars any state or local prosecution for failure to register.
No helicopter in existence (or that is at least airworthy) has the range. Not 1200 miles. Not even an MV-22 has that range. Only helo ever produced that does is the AH-56 which was never mass produced and remaining aircraft are display pieces at Army posts.