It would seem so, but nobody plays it that way, and it has been argued heavily.
I would play towards the side that doesn't break the game.
Plus, the extra damage is a cost.(p48) "These costs must be paid when the trigger is declared or no portion of the Trigger may resolve." It is something payed for, not caused by the action. It is also stated as not a portion of the trigger.
But probably most importantly, if you just take the damage, ignoring incorporeal, without passing the wound, you don't have to argue anything, and you can get on with the whole point, which is playing the game. At least until Wyrd gives us a ruling.........