The question isn't so much if someone is an addict before or after they abuse drugs, but rather how do you correct the behavior?

What motivates a drug addict? The desire to be deviant and break the law?  Or have they become mentally ill and are unable to help themselves? The answers to these questions should determine wether incarceration or treatment will be more effective in preventing the behavior when they are released, which is what we all hope happens with the tax dollars we spend for crime prevention. 

There's interesting research that points to treating addiction versus jail time in being more effective at putting people on the right path. It's easy to think "bad people go to jail" but you have to ask what the point of jail is. Is it just to remove the undesirables from society or is it truly a "correctional facility" that's supposed to reform people? Probably a bit of both, but I think we all want to see people who are released to not be a danger to themselves or others.