You can always risk it, but face it, it's illegal.
Illegal as in against the law.....as in getting an Immigration violation and potentially banned from the US for several years.
Banned as in not allowed in under any circumstance, not even with a visa.
Illegal as in potentially a big fine for you and for the school that trains foreigners without proper documentation.
All it takes is for somebody to mention that school XXX is training foreign students.
Foreign students need to enroll with a school that has visa approval.
The school will sent you an application form that you take with you to the US embassy.
The process is described ( amongst other places) here:
http://www.eaa-fly.com/2.0/en/MainTrainingVisa.html