When under an addiction the addict still has free will, at least to a small extent they do. They are still able to make choices and are able to decide what they will do for the day. Yes, it is likely they will just spend the day feeding their addiction but they might not.
Nobody has absolute free will over anything or absolute lack of free will. If addicts really had no free will then nothing short of strapping them to a chair while they ride out withdrawal would work, but typically less drastic solutions can help addicts. Getting help doesn't mean they don't have free will either, anymore than getting support in anything else in life means you don't have free will. And as addictive as cigarettes are some people just quit cold turkey and that's that. So clearly there is free will.
I was under my own free will the whole time! I chose to do drugs, I chose to prostitute, I chose to stick needles in my arms. IT WAS ALL MY CHOICE! Being a drug addict is a choice that people make it is their OWN fault, no one else's. To think that it was anyone else's fault is ridiculous!
No, under an addiction, the addict does not still have free will. Users who have been addicts for a while no longer have any moments when they are entirely drug free and lucid. As the length of their addiction continues, the frequency or amount of drugs usually increases also. Their sole reason for existing becomes their next high. The addiction robs them of free will. They become enslaved to the addiction and it takes over their life and personality. They are no longer able to make a decision to become drug free.
Drugs and alcohol, for instance, take the body to extremes and cloud thinking. In this clouded thinking, and need for more drugs, most people cannot make clear decisions. Any decisions they try to make are usually affected by their need for more of their addictive substance. That is why intervention and rehabilitation are necessary.