Depends on what you mean by "cannot be controlled." Once the brain has remapped, the activity cannot be healthily engaged in in moderation. It can be "controlled" by total abstinence, if the person realizes the problem, admits they have a problem, seeks and receives the support of others in abstaining from the addiction, etc.
There's a huge difference between (1) realizing the habit is destructive, and (2) having the understanding of addiction and the external support necessary to fight it, and availing oneself of that knowledge and those resources. Essentially all addicts realize the habit is destructive. Not all addicts fit #2 for various reasons.
No. It defines them as having a problem. Not as having weakness of character.
Though as noted above, I'm not an objective person to answer the question, because we're talking about me here. And while I've got some problems, I'd like to think I don't have "weakness of character."