I think Jerry's right -- my EP when going over possible scenarios, said, the procedure that makes it so you don't feel the afib, because you are not aware of it, makes it necessary to stay on blood thinners.
From the little I know, AVNA makes one pacemaker dependent. Is this true for your case? That said I have also read it the AVNA was treatment for AFib, it is possible that the AFib will continue, and perhaps not be felt by the patient. If AFib continues I believe one would have to continue to take an anticoagulant, Warfarin.