Perhaps not directly. But the difference between public school and private schools is impossible to overstate; and it is strongly correlated to houses with one full-time working parent and one part-time or flex-schedule parent. The tuition (almost regardless of how much it is) immediately filters out financially overwhelmed and un-involved parents. Then even for the parents that can afford it, some schools also have involvement quotas that will cause a pair of full-time parents to drop out. Morale and motivation in private schools is extremely high, akin to that of people working in good jobs; which counts for about two or three grade levels.
The end result is that you have a kid who is surrounded by children who know nothing other than a 7-day week of school, getting up at 5am to wrap up missed studies, music lessons, sports. Even if they do spend a bit of time goofing on iPads and watching TV, it is nothing like what happens with parents who can only show up long enough to sleep and go back to work.
Even people who are poor will try to move their kids into the better school districts. A few will even break the law to do it, with few regrets when they get caught. (You can get sued by the county for doing this.)