In the short term at least, yes. But considering American schools get most of their funding based on students' academic performance – and low grades means they get defunded and have to cut things like schoolbuses, supplies, and education programs & quality – it's a very short-sighted thing to do for schools which don't have peak student performance (and most schools overpaying coaches and underpaying teachers don't have good student performance). Not to imply that you were saying that this isn't the case
And that money gets plugged right back into the sports teams. When I was in high school, our theater auditorium where we did our plays was literally falling apart. We had to tape off seat rows that were unusable. But the football team got new locker rooms with jacuzzis in them.