What I mean is, I suspect it will simply not work. It might break a single block like a regular axe, but I guess that the "special" mechanism of "all connected log blocks break and are magically transported into the player's inventory" will not work, because there is no player's inventory for them to go to. The obvious retort to this is, "but a harvesting golem has an Axe of the Stream and no inventory, and that works", but my reply to that would be: "No it doesn't have an Axe of the Stream, it has a Harvesting Core, which is a different item with different mechanics". I could be wrong - maybe Thaumic Tinkerer has specific mechanics to deal with an Axe of the Stream as a special case, but I think we'd have heard about it by now.