Out of sheer cussedness I once made up two dozen arrows with random locations of the fletching. Each arrow was either right wing or left wing and the complimentary jig to the fletch, but the placement in relation to the nock orientation was random. Some came out with the cock feather against the bow, others with one hen feather against the bow, some with two hen feathers against the bow, and minor variations of all of the above.
Each arrow had a roman numeral written below the cock feather, I through XXIV. I kept track and only one of the arrows flew funny. It hit considerably lower than all the rest and consistently. I weighed it and the shaft must have been a mis-weighted "blem" in the bunch, it was almost 100 grains heavier than the rest. Nice thing about these arrows, they got me over the panic of trying to get the arrow nocked with the cock feather located "correctly" when I was making a quick follow up shot.
I think matching the spine to the specific bow is much more critical. Bare shaft shooting this double dozen made them the best shooting arrows I have played with in the 8 years I have been goofing with bows.