Speaking only from our experiences last year, braces have to come off before in-processing. That said, WebGuy posted photos and a blog last year about how all the Basics went to the dentist and had an ortho consultation if needed during BCT. I know some people were offered braces. I don't know about cost because my DS didn't need them.
Similar in concept, you have to finish all rounds of treatments and medication, etc. before in-processing, as well. This meant for our DS that he could not finish his Accutane (acne meds).
Your ALO should be able to guide you through such questions.