Anger is dangerous for addicts. The 'high' that we get from rage can be, in many ways, its own drug. That's why some people can become 'addicted' to rage.
I would say, 'yes and no.' Clearly, anger does not present the same brain chemistry that substance addiction does, and I have not seen evidence that people who become angry often or violently have an 'addict brain' the way alcoholics, drug addicts, and porn addicts do when examined by an MRI. But, one can also lose control over one's ability to control rage.
And, just like substance abuse, rage is a response to powerlessness in the face of a threat. Watch an episode of 'COPS' and the #1 excuse criminals give for fighting with police is "I was scared." Anger and rage are responses to terror. They are not hopeful dispositions.
I think this is critical in understanding the difference: the substance abuser has a 'hope' in his drug, whereas the rager has no hope other than destruction of what he would otherwise 'use.' This is also why Envy and Anger are close relatives: both are destructive tendencies, yet each has its unique calling. Envy is aimed specifically at people, where as we can get angry at even abstract institutions and inanimate objects.
Envy can also be far more subtle than the fearsome bile of Rage. We can often act in the most sinister a subtle of ways under Envy, whereas true Rage is impossible to conceal or understate.
Fear is always about a loss of control, and it is the loss of control that is central to addiction. The difference I think has to do with the restoration of hope. The true addict must release one hope in favor of another, whereas the envious rager needs only embrace a hope. Letting go, anyone who has tried can tell you, is really hard.
This is why, in my opinion, that Anger Management therapy can often be conducted without a spiritual program. The challenge is far less daunting. The rager need only embrace the idea that he can have hope of not going to jail again if he stops acting out, and so this hope becomes impulse control he needs. The trick is to catch the thinking before the onset of the emotion, or at least early enough in its cycle to divert it.
Addiction is far more complex and resistant. This is why psychology alone can't cure it or even really treat it at all. Psychology is only effective in treating the contributing personality or emotional disorders that arise from or contribute to addiction, but addiction requiers a spiritual treatment in order to make this shift in 'hopes.'