No...you're thinking boot camp. Military boarding school is something completely different. http://www.militaryschoolsforboys.org/content/military-school-vs-boot-camp.html
It depends on the school. Primarily, these schools are designed to instill discipline, organization and the ability to understand and follow a chain of command. They are led by official military channels, with teachers having to be locally certified and cleared by the county Board of Education, and senior instructors up to the commandant having to be directly cleared by the Army, etc. and holding an official rank of a light Colonel. They're not necessarily akin to the old "boarding school" we grew up hearing about. Education provided focuses a lot more on military history, frequent mustering/inspection, proper uniform maintenance and the like. But it's not just for kids that don't behave. It's also for kids who have an interest in the military, or whose parents are career military folks and feel that putting their kids in such an institution provides an advantage for their future. But yes, there are the ones that are enrolled for disciplinary reasons. Our martial arts academy teaches a judo class at a military academy each semester and we have intimate dealings with it. This is at the high school level. I am not, in any way, saying Trump has any such skills or military training. I am merely speaking to the nature of military academies at the high school level.
That would be funny if it wasn't for the fact that Trump is a coward draft dodger who doesn't even remember his excuse for avoiding serving the country.