I think there is a link between the two because many people that have ADD or ADHD often go undiagnosed especially as adults and have a tendency to self medicate.
Like my sister, who has ADD took speed during her school years and college. It helped her focus and then turned her into an addict.
Just one example.
She still has ADD, has been clean and sober 10 years and is married, has a son and is expecting her 2nd child. She is a success story for sure.
I think there is a connection between mental illness and addiction .In my opinion addiction is in part a mental illness