Not necessarily.
It's vital that you disclose both of these charges when applying to the Academy, and you should expect to be thoroughly grilled as to the details.
Have a solid and sincere explanation ready about the stupidity of your teenage years, your subsequent growing up and getting over being an idiot, and a solid record of being a decent, law-abiding, tax-paying, helping-old-ladies across the road citizen.
No guarantees, of course. Your eligibility will vary by jurisdiction.

