This is, of course, a matter of opinion. My own opinion is that it would not be right to enact such a law.
One reason for this is that this proposed law does not differentiate between an alcoholic who is recovering and one that is not. Of course, any alcoholic is at risk of relapsing and becoming an active drinker. However, this does not mean that recovering alcoholics should be treated just the same as alcoholics who have not done anything to fight their addiction.
Another reason for this is that such a law would be a chilling extension of governmental power. In the early 1900s, the government often used various pretexts for sterilizing people in the name of eugenics. This is not the sort of power that we want the government to have. It is too easily abused.
Finally, having a child is a fundamental human right. It would be unjust to take this right away from someone simply because we suspect that they would end up being a bad parent. Taking away basic human rights just because we are worried about what might happen in the future is a very bad idea.