While it's possible, I doubt it happens often. A kid would most likely be attending a school from a different neighborhood if the parents want him/her to specifically be at that school, or if the child was already enrolled at that school and they moved to a different part of the city. Boston has a school bus system that as far as I know follows routes closest to the school without overlapping much from the areas set by other schools. I don't tend to ride the trains much in the morning, but I can say that I don't COMMONLY see children riding the T to get to school. (Btw our subway system is always called "The T" by locals.) They're either taking busses or their parents drop them off. Then again, I also live in the major college student area of Boston. So my area tends not to have many permanent residents or upbringing families. You see more of that in Cambridge (Red Line,) Brookline (C/D Lines,) Charlestown, and Jamaica Plain (Orange Line.) So I can't exactly say my observations on that matter are 100% accurate.

BTW Fun Fact: [link] -- that's the school from that older Fox show "Boston Public."