I'm Planning to Put on Braces, Will That Change my Vocal Chords, Range and Tone Once I Remove Them?

Interesting question!  The short answer is, no, the braces will not affect your voice, range, or tone after they are removed.  When you first get the braces your lips will not slide on your teeth in the same way they do now.  As a result, opening your mouth wide and articulating your lips to influence sounds might be affected.  You should be able to adapt to that after a few weeks.  If your orthodontic problem is amenable to correction by Invisalign this lip sliding issue would not be a problem at all ... you could remove the aligners for a few hours a day while you sing.

Having braces should not have any effect on changes in your vocal chords, range, or tone once they are removed.  Good luck with your orthodontic treatment....and you have nothing to worry about