You can complete his quest (go to heaven, remove your names from the scroll) but you can't complete his sidequest (destroy the tree), as it requires dialog from his sword to trigger. Unless you pocket plane him in and he has the sword; I'm not sure about that.
I somehow managed to miss quest three of Dorn's (where you can get the patron change) despite having him in my party in SoA, and thus I got invalid reply error at the tree and couldn't corrupt it. Pity, that.
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You can do new NPC quests in ToB if you have never met them in SoA.
Analyzing these facts, I guess you don't need to have completed Dorn's quests in SoA in order to be able to do his questline in ToB.
Another story is if you completed the quest in a particular way and he still has a patron in ToB you'll have an additional task during his quest.
I somehow managed to miss quest three of Dorn's (where you can get the patron change) despite having him in my party in SoA, and thus I got invalid reply error at the tree and couldn't corrupt it. Pity, that.