Can I direct wire an under the counter light into the LOAD terminals of a kitchen GFCI outlet?
Nope -- kitchen receptacle circuits need to stick to kitchen receptacles

You'll have to run the lights on a different circuit to meet Code, as putting lighting on a kitchen small appliance branch circuit violates NEC 210.52(B) (in particular, 210.52(B)(2)).  Note that "outlet" by itself in the NEC means any place where power is supplied to a device (whether it's a luminaire, a receptacle, or a piece of hardwired equipment), not just receptacles.


  (B) Small Appliances.
  
  (1) Receptacle Outlets Served. In the kitchen, pantry,
  breakfast room, dining room, or similar area of a dwelling
  unit, the two or more 20-ampere small-appliance branch
  circuits required by 210.11(C)(1) shall serve all wall and
  floor receptacle outlets covered by 210.52(A), all counter-top outlets covered by 210.52(C), and receptacle outlets for
  refrigeration equipment.
  
  Exception No.1: In addition to the required receptacles
  specified by 210.52, switched receptacles supplied from a
  general-purpose branch circuit as defined in 210.70(A)(1),
  Exception No.1, shall be permitted.
  
  Exception No.2: The receptacle outlet for refrigeration
  equipment shall be permitted to be supplied from an individual branch circuit rated 15 amperes or greater.
  
  (2) No Other Outlets. The two or more small-appliance
  branch circuits specified in 210.52(B)(1) shall have no
  other outlets.
  
  Exception No. 1: A receptacle installed solely for the electrical supply to and support of an electric clock in any of
  the rooms specified in 210.52(B)(1).
  
  Exception No.2: Receptacles installed to provide power
  for supplemental equipment and lighting on gas-fired
  ranges, ovens, or counter-mounted cooking units.