"What does NJ statute say about this (if anything)?"
From what I have read, bearing in mind that I have read the entirety of the statues as a "layman (former) resident with a sincere interest", the statutes seem silent on the precise subject. The statutes seem to deal specifically with purchase (on a pistol permit) and inheritance, but not purchase out of state of an unregulated item and then subsequent importation.
From a practical standpoint, it's the most common way to procure BP items in NJ. But posession outside of the home requires the same NJ state firearms ID, transport requirements directly to/from range, etc.. and again, from a "practical" standpoint, if you act with one the same way that you would act with any other "legally procured" firearm you are not likely to be hassled.
But... in the end... "Tell it to the Judge" after a prosecutor takes the case. I have absolutely no doubt that if you misbehaved with one (IE: had them taken during a domestic "violence" incident), that they will use anything they can to try to make a case, and your "unregistered" BP arms would be a point to argue.
There IS a voluntary form to register a firearm in NJ... "probably" the way to perfectly legalize a BP arm purchased out of state would be to use that process.
A lawyers eyes on the statutes with some introspective comment would be most welcome.