Hey Jed:)
It might but if the instructions are correct, there are only 4 "types" of settings to choose from, the gamepad, standard stick, a Thrustmaster, and a wheel.
Now I think AH can recognize additional sticks, so theoretically, multiple sticks in AH would work. Now concerning that adapter, I'm guessing that it's work for that setup too, but the input to AH would be limited to what the adapter allows. Meaning, if the adapter on the standard stick setting allows for an x and y axis, and only two buttons (sorry, I can't recall exactly what it controlls off hand), then only those buttons and stick inputs would be sent to AH and all additional buttons would just be ignored.
That's my guess anyways. Maybe check out the Thurstmaster setting...there may be more options there.
Hope that helps some.