You are correct about the CESA teams staying active during the HS season. Usually it is because they are getting ready for regionals. I can tell you that their coaches would not tell kids that they could not play HS soccer, the coaches I know encourage the kids to even play other sports so that they keep their fitness levels high.
I can also tell you that the HS programs where many of the top players in the state play--Mann, eastside, riverside, wando, irmo, BE, Christ etc.. have training that is just as good if not sometimes better than a lot of the academy and club coaches offer. The one invaluable thing they provide is playing for school pride and allowing the kids an opportunity to excel in front of their friends not just their parents.