No, it is not. Period.
The AA12 as you have seen it in its current configuration was manufactured after May 19, 1986. Therefore it cannot be legally transferable. Any fully automatic firearms must have been manufactured AND REGISTERED as transferable NFA firearms before May 19, 1986 in order for a civilian to be able to own them.
This is Federal Law.
You MAY find an old Atchisson Assault 12 (the predecessor and parent of the AA-12) which is a registered transferable, as the Atchisson was manufactured sporadically from 1973 to 1985 or so, mostly as demo models for police departments. When Max Atchisson sold his patent to Military Police Systems in 1987, that was the end of the original Atchisson. Since Military Police Systems didn't even manufacture the modern AA-12 until far past 1986, having not even had the patent rights until a year after the cutoff date, it is legally IMPOSSIBLE for an AA-12 to have a transferable status.