Since it can result in unpredictable blackouts, I kind of suspect that the answer is no. Sudden incapacitation is the one thing the FAA will not take a chance on. Diabetics can hold a 3C, but they have to follow special procedures to monitor and control blood sugar in flight. If it can be controlled reliably with meds or pacemakers, then maybe a 2C, but I don't think there are any meds for that. Beta blockers don't help IIRC.
I would talk to these guys or another similar consultant outfit, they will at least be able to give you a definitive answer.
Aviation Medicine Advisory Service -- FAA Medical Expertise -- Our Physicians...Your Solution!
Best of luck with this.