I'll be honest' I'm not famillar with NFA paperwork period let alone as any would regard to a suppressor. However to answer your question I would say, NO unless the paperwork said you couldcarry the suppressor in public and/or use it in public.
Here is the part of the law you may be asking about.
T.C.A. 39-17-1302Prohibited weapons. —
(b) It is a defense to prosecution under this section that the person's conduct:
(7) Involved acquisition or possession of a sawed-off shotgun, sawed-off rifle, machine gun or firearm silencer that is validly registered to the person under federal law in the National Firearms Registration and Transfer Records. A person who acquires or possesses a firearm registered as required by this subdivision (b)(7) shall retain proof of registration