I don't claim to speak for all addicts, but this is not how I would describe my experiences, at least not under my conception of "free will".
I "wanted" to stop doing drugs in the same way a lazy person "wants" to go to the gym more. whenever the moment came to actually do it, I had to admit that I didn't want it nearly as much as I said I did. sure, I wanted the "outcome" of quitting, but in the meantime, I really wanted to keep doing drugs. so I did.
every day I had a clear goal in mind: getting money and acquiring drugs. I was fairly strategic in pursuing this goal; I was even capable of abstaining for a while (eg, to pass a drug test) if it increased the security of my future supply.
I was in and out of treatment for a while (primarily to appease others), but I ultimately stopped doing drugs because I didn't want to anymore. this happened rather suddenly, over the course of just a few months. a few areas of my life improved simultaneously, partially through my own efforts, but partially just luck. I now lead a fairly normal life.
anyways, the reason I type all this out is because I really don't like it when people describe addition this way, especially if they aren't/weren't addicts themselves (not assuming anything about you in particular). depending on what you think "free will" is, it may be more or less accurate. but it is usually a prelude to an argument about how addicts aren't competent to make choices for themselves and how society should Do Something About It, usually involving curtailing the freedoms of people unfortunate enough to be identified as addicts. addicts don't need to be controlled or disciplined (unless they are hurting others, of course). they just need to reach that tipping point in quality of life where drugs don't seem so appealing. at least that is my belief, based on my own experience and observations of others going through it.