A school permit is only valid if it is issued by the state. In that case, it is considered a learners permit.
It really matters which insurance company you are covered with. Each company has their own internal rules pertaining to unlicensed drivers. You should check with your agent or company for information regarding their specific underwriting rules. CarInsurance.com writes with some companies that will not cover a child with a learners permit unless added to your policy. We also write with companies that will cover a driver with a learners permit.