Being a LEO who deals with these types of firearms on an infrequent basis, I would say that the burden of proof is on you to prove that the guns are legal, not the officer. NFA weapons are always registered with the ATF and maybe the police department where (and if) you had the head LEO sign off on it, but other jurisdictions won't have access to the info right away. Every short barrelled weapon or homemade silencer I have ever dealt with has been illegal, but the suspect will claim they didn't know or have the paperwork at home. I have seen people with registered NFA weapons "lend" them to their friends for extended periods of time, which we know you cannot do. I have even seen fake NFA paperwork for an unmarked auto sear. But the suspects usually have no idea how the NFA process works, where a legitimate person knows the process very well. Most states have laws outlawing NFA weapons without federal approval (ie tax stamps), so an officer does have the duty to fully investigate. Basically my point is that just saying you have the paperwork won't work in most cases. If you were an officer, would you like to be known as the guy who got duped into letting a "dangerous" silenced weapon walk when in fact it turned out to be illegal?
My suggestion to you would be to have a copy of your paperwork handy. In reality, an officer could arrest you for not having it, but could very easily just impound the weapon and hold it until the paperwork is presented. It took alot of effort to get the weapon, don't risk it by not having a simple piece of paper saying its OK.