There are two very different issues here. One is the physiological effect of the alcohol; the other is the psychological effect.
Other posters have commented primarily on the former issue, which is fine.
As to the psychological, however, the matter is very personal. It depends on what sort of recovery approach one is taking, and how one thinks about one's current condition. For some, the explicit presence of alcohol is a very serious matter: it's as though the dish were saying, "hey, alcohol tastes great, and it can't be replaced, you need it," and for some people that is about the worst message to receive. One recovered alcoholic I know feels this way so strongly that he refuses to drink alcohol-free beer, e.g. O'Doul's. And there are lots of other ways people approach their recovery and stability.
Thus, if you ask me, it is simply not appropriate to make any decisions about this question yourself. Make your dishes the way you want to make them, and clearly label anything that has beer, wine, or spirits in it. If someone requests alcohol-free and you accept the request, avoid anything that you would in any remote way consider alcohol, in any quantity. Don't give advice or comment, such as, "well, all the alcohol cooks off anyway," which first of all isn't true, and second is quite likely not the point.
A great many recovering alcoholics think of their condition as a chronic disease that requires constant prophylactic treatment. If someone were allergic to strawberries or peanuts, you would not be thinking, "well, would just a little bit hurt?" From your point of view, treat alcohol precisely the same way. The rest is up to the customer, and is not your business.