Hi nitroxbubbles,
I am not aware of such research, and I very much doubt there is any. As you likely know, Addison's disease (AD) is not a common condition.
Left untreated, AD can prove fatal in the event of dehydration, accident, infection, surgery or other stressors. Incompletely treated/stablized, it could pose a number of threats to safe scuba.
With careful replacement of the corticoids otherwise absent in AD, an individual without complications or other disease can lead a pretty normal life, and in fact there are people with this condition who do scuba dive.
Of course, illnesses that can arise on dive trips, such as upper respiratory infections or GI disorders involving vomiting or diarrhea, pose special risks for the AD patient. Keeping properly hydrated & electrolytes in balance also requires their extra care while diving. Additionally, it would seem prudent for them to avoid diving that is heavily physically taxing.
Any individual suffering from this disorder will need medical clearance from their physician. Even if cleared, they will need to take special precautions, such as carrying identification stating the condition & steps emergency personnel should consider in the event the AD patient is unable to assist them. When traveling, persons with AD often carry syringe & an injectable form of cortisol for emergencies.
This is educational only and does not constitute or imply a doctor-patient relationship. It is not medical advice to you or any other individual, and should not be construed as such.
Hope this gets you started.
DocVikingo