This whole thing comes off as condescending and patriarchal, though, and I'm not sure it's really going to do anything at all to curb the problem, anyway.
That's sort of my feeling on it, too. Particularly given the fact that the time where you're most likely to not know you're pregnant is the time before the embryo has actually implanted into your uterus (i.e., before you've missed a period or had any pregnancy symptoms) and at that point the embryo isn't exposed to alcohol from your bloodstream anyway.
Add to that the fact that, when you actually parse the data, it's not the women who have one drink occasionally during pregnancy who have babies with fetal alcohol syndrome. While we don't know a safe level of drinking, the risk seems to be really heavily associated with binge drinking and/or drinking heavily, regularly, over a long period of your pregnancy (especially the first trimester).
I'm sure there are cases where women would like to have access to a pregnancy test to know whether they can drink or not this month. I'm not convinced that it's the lack of pregnancy tests at the bar that determines the vast majority of FAS outcomes. You'd do much much better by actually addressing the social, health, and economic factors that drive alcoholism and unhealthy drinking behaviors.
Meanwhile, stuff like this and many of the personhood laws for embryos and fetuses make me increasingly concerned about issues like the prosecution of women who have miscarriages.