I think it might make sense in some general ways. I doubt there's any difference between a late-august and an early-september baby, but I could see there being a (moderate) difference between a january baby and a september baby. Mostly because of seasons influencing the pregnancy/early childhood experiences, and also being months older/younger when school starts (older kids might have an easier time at least at first).
Sorta similar to the birth order thing. It does predict a few general trends, although not much that is really conclusive.
women living in cold climates that conceive in the winter not receiving as much vitamin D via sunlight in the early stages of pregnancy, possibly affecting her fetus.
But they didn't say what sorts of horrible effects this might have had on me.
I've heard of this in terms of success in athletics, where some kids have 11-10 months of developmental advantages when they're younger which leads to placements in advanced leagues early, but otherwise I'm not sure if there's too much to it.
I think it's been understood for a while that there is a mild correlation between careers and the time of year of one's birth. However, it is more than adequately explained by various minor factors (some of which are mentioned in the article, others including the interaction of critical development periods with seasonal environments). Ascribing it to the stars seems a little ridiculous, especially since the effect seems to be reversed for the southern hemisphere.