If I'm right - you're asking if it's possible to use the old AR for the Gamecube (which IIRC was a small CD & a memory card that plugged into a Gamecube slot) on the Wii
Bad news I'm afraid - it won't work, especially if you've upgraded the firmware on the Wii
I had one when the Wii first came out & it didn't work (although I'm sure it did work on some older games BEFORE I upgraded the firmware).
I contacted the manufacturer (Codemasters) & their answer was basically - "No chance. The device was built for the Gamecube & not for the Wii. the hardware is designed differently" (admittively it was many years ago & I may of forgotten most of their reply - but you get the gist of it)
I may be wrong - & perhaps some1 else can confirm this