Interesting question. I admit I had to look up what boudoir meant.
I think you would have to read through the statues to determine what defines a firearm. Is a receiver without a bolt a firearm? The AR lower is the serialized part and you do need FPID to purchase it. I don't know.
However, being NJ has the Graves Act which provides for mandatory minimum sentences for firearm crimes, I wouldn't take a chance that any LEO you come across would know the technical differences in the laws.
Not to mention, the plain view exception to the fourth amendment would give LEO's the right to search your car if they saw the gun on your rear seat. I would lock it in the trunk or a case and avoid a very big and expensive headache.
Remember NJ Appellate Judge Baime in State v. Pelleteri: "When dealing with guns, the citizen acts at his peril."