Nope. Both sides of the same feather aren't identical, and you only use one side. Suppose I should never say never. Some folks have probably used the other side as well.
Anyway, after they're split, you use the larger side of the feather for fletching. That's the trailing side. Envision the feather on the bird with its wings outstretched. Viewed from the front, you want the part of the feather that is on the back/far side of the quill. Hope that makes sense.
Feathers from the left wing need a left wing clamp, and feathers from the right wing need a right wing clamp. Don't mix right and left wing feathers on one arrow.