i wish uninformed people wouldn't give advice.
im in an ivy league grad school and come from a family of ivy leaguers who have gone to medical, dental and law schools. for that reason, i won't give advice about business school, because i know little about it.
a BTL can get you into law school, but if you want to get into a good one, you need a great GPA and you need to ace your LSATs. harvard will take a BTL with a great LSAT score, and columbia is warming up to them. not sure about other schools. the problem is that you will definitely struggle in school if you don't have a basic education. you can still succeed if you're smart, but i really can't recommend a good education strongly enough. you need excellent reading and writing skills, and basic finance/economics/business classes will be helpful. with law, you want to get into the best school possible, because the job market is tough. getting a BTL and getting into an average law school might get you a job, but not at a NY firm that pays market. so it depends what you're aiming for.
with medical and dental school, the job market isn't as scary, but it's much harder to get in. a BTL will put you at a severe disadvantage. that's not to say you won't get in, but it's not a risk you should take. you need a strong science background to get admitted, and you'll need that education to do well once you're in classes.
when you're applying to any graduate school, you want an honest resume that's padded with leadership positions (in clubs or off-campus) and extracurriculars (hobbies, volunteering)
you need to think about what you and your son want, and speak to friends and family who have done things like this.
best of luck.