I'm sure there's a link between poverty and people becoming drug addicts.
In my experience (of acquaintances, friends and family, not first hand) there's also a strong link between poverty and not being able to come off drugs.
I'm not sure how simple the cause and effect is though. Lots of the factors that can cause poverty could also be directly responsible for addiction, without necessarily having to cause poverty first. Also it's really obvious that addiction causes poverty too.
I'm not disagreeing with you at all, i just think there's levels of causes within inequality and poverty.
For example, if we had functional mental health services we could tackle some of both drug addiction and poverty at source.