No, the kill is awarded to who does the most damage. Thing is, different pieces "soak up" more damage before failing than others. If you sweep wingtip to wingtip with .50 fire, you've actually done a good bit of calculated damage to the aircraft even if nothing has failed. Someone then comes by and fires a couple rounds in an expert shot into the wing spar and it snaps like a twig. The amount of damage to that wing spar is less than the amount of damage that you dealt to the whole airframe; you get the kill.
Note that explosive rounds will deal damage to many parts at the same time.
This is the reason a 110 can fly around stealing all of the kills on tanks. For some reason, tank treads have an amazing "hardness" to them; they take a lot to kill. The 110 buzzes around dealing massive explosive damage to the tracks that do not die. Somebody in a Tiger puts an 88mm hole in the driver's head. That 88mm killed the tank, but was a fraction of the calculated damage the 110 dealt to the tank. Ricochet rounds do not count in this area, but rounds landing next to the tank treads still have the "tiny bomb" effect and deal damage.