Does the NEC allow a 14ga branch on a 12ga circuit?
Is it within the NEC to wire ceiling light fixtures with 14ga NM from
  a switch wired with 12ga NM, where the power originates at the switch
  and the ceiling fixture is a branch?
  
  The breaker protecting the circuit is 20 amp.


Absolutely not. If the branch circuit is 20A then ALL the wiring on the circuit must be at least #12cu. 

Yes, there are convoluted tap rules but they would not apply in this installation and IMO are not even worth mentioning.