Being able to milk the body for its last drops certainly seems to require what one might call a strong will.However, when looking at, for example, professional athletes, it's not uncommon for them to reach the goal on pure willpower, even if their body has practically given up. Don't you feel that if someone is headstrong and determined enough that they can fight an addiction as well? I'm not saying that this is definitely the case, but it's a line of thought to follow.
I think a strong will is probably highly correlated with an ability to maintain high levels of attention for a period of time, something that varies from person to person, and is a useful skill to be cultivated.
There are a couple things things that should be said though:
One is that if we are to view it as a cognitive skill, then that changes the way we judge people. We tend to fault people for having a weak will, when in fact, at that point in time, they simply do not have the skill to be able to exert such a will.
The second point is that i'm not convinced that the use of this skill should be the front line of attack in dealing with an addiction or dysfunctional behavioural pattern (see the Gollwitzer reference in the quoted passage for an example).
It almost certainly has its place - perhaps in overcoming a transient craving - and there may be people who can overcome huge obstacles through exercise of this skill alone.
A more sustainable solution is to reprogram the mind in a more systemic way. Bad habits and addictions are in some way a manifestation of positive feedback systems - vicious cycles of cognition, affect, and behaviour.
A systemic solution is thus needed - one which can actively reshape the dynamical space so that there is no longer an "attractor" associated with the undesired behaviour (sorry if this paragraph doesn't make sense).
A strong will may be able to prevent the brain from falling into that attractor, but a strong will alone will not get rid of the attractor.
Think of a metal marble rolling around a bowl - the path of the marble at the basin of the bowl could be understood as the attractor. Think of will power as a magnet which can stop the marble from reaching the bottom of the bowl. Useful for a while, but wouldn't it be more powerful to also be able to reshape the bowl?
I should also note that I haven't studied this particular issue in depth - my knowledge of addiction is fairly limited, so I'm drawing upon limited research here.