Your description should have included more details, without those it's pretty much impossible to give you any advice. For starters, are you extending your study permit? Or are you applying for a new one?
IF you are just applying for an extension, it shouldn't matter as you will have implied status. If you are applying for a new permit (means you never had a permit before), then you cannot start school until your permit approves. I'm not sure about high school, but for universities the department will not let you register unless you have a valid permit. IF your school allows you to be enrolled without a permit (which i doubt) then yes, you can start going to school after they approve your study permit.