Yes, my duplicate would think the same way as me.

In a world that has duplicators, my duplicate would not claim to be original without evidence one way or the other.

In our real world, if a copy of me were made using "magic", both versions would believe themselves to be the original (at least at first). I had this kind of very specific scenario in mind when I said both would claim to be original, but did not explain this in the earlier comment (inferential distance and all that).