An alcoholic who is offered the option of surrendering their judgement, their will, and their decision-making to the programme will not drink, as that surrender entails the offering of a sufficient substitute.
Withholding surrender is an act of the will. This is deliberate.
If surrender is withheld, the person will not necessarily drink straight away. They might wish to stay sober, at least in their higher self, and, whilst that higher self is the more powerful faction, they will stay sober. As soon as the lower self, which includes the alcoholism, wishes to drink and asserts itself, because self, in general, is still the arbiter of judgment, will, decisions, and action, the person drinks. They have 'changed their mind', or, more properly, the centre power within the mind has shifted from the higher mind to the lower mind. What looks like volatility is really a regular and predictable shifting between the two parts of the mind, in the greater context of a stability: the stability of self, in all its forms, being the only god the individual knows.
If I drop my iPhone on Great Eastern Street and do not pick it up, that is an act of the will. It could be one minute or three hours before a car drives over it and destroys it. I am powerless over when the car drives over it and destroy it, but I'm not powerless over whether or not I pick it up when I drop it.
If I take charge and enthrone myself as my own highest authority, that is an act of the will. When, how, and under what circumstances the drink takes place is something over which I am powerless, because my act of the will is really a surrender to a more powerful force: the welter of conflicting emotions and drives within self. In willing my surrender to self, I am relieving myself of will and turning it over to self, which is now in charge.
The only way this can be reversed is to perform a new act of the will, namely to turn my will and life over to God, against which self is completely powerless. The I can calmly take the will, like a plug, and plug it into a new socket at any time.