What you are asking about is a "letter of medical necessity" to have
your medical insurance pay for what is seldom if ever covered by major
med/hospitalization coverage.
    While this mechanism exists in theory, I am not aware of it ever being
successfully used for orthodontic treatment.  I have heard it tried more
often in severe skeletal deformities where the treatment includes
orthognathic surgery (to move segments of the jaw(s) surgically in order
to improve the bite and/or facial appearance).  Even here, it is
difficult to get coverage.  For routine orthodontic treatment (as
opposed to surgical orthodontics) I thing the chances for coverage are
very remote.

Steve