Scott Adams thinks it's important:
My hypothesis is that the month you conceive is the most important factor in a child's success. And no, I don't mean horoscopes are important. What matters most is how old a kid is for the class he is placed in.
Macolm Gladwell described in his book Outliers how the older kids in a class are identified as gifted athletes, when in fact they are simply older. Coaches give more attention, training and resources to develop the perceived talents of older kids, thus widening the gap over their younger classmates.
When I first heard about the birth month advantage, I assumed it didn't matter much for ordinary kids who had no plans to be professional athletes. But consider any kids you know, and how much they change, mentally, emotionally, and physically in the course of one year. The youngest kids in a given class are at a huge intellectual disadvantage compared to the oldest.
I was always the youngest – born in August, and put into elementary school a year early because my mother was hospitalized for depression. I kinda liked the challenge of competing with older kids.