The left analog stick can only be used on games that used analog controls on the 2600 such as the paddles and driving controllers. Joystick moves are strictly assigned to the D-Pad.
There are two versions of the Wii Classic Controller. The "Pro" version (pictured in your post) is the second version and it required some additional work to make it fully compatible with homebrew on the Wii. This was up to each homebrew programmer to add it to their applications. Some didn't add it (O2Em does not support either version). In the case of Wii2600, this left the analog sticks non-functional. The older version without the "handles" will be fully compatible.
I picked up a nice Wii with BC at my Goodwill for $13. No controllers, but I just used the second controller from our other Wii. I've been wanting to softmod my Wii, and now I've got no excuse. Is there a trusted walkthrough somewhere that elaborates on the process Jinks described?
PacManPlus is a great programmer. I have been very often amazed at the rate he produces new games. He has helped to show the potential fun that was hidden away inside the 7800. He took the time to read feedback about his WIP games. He shows that he truly cares for this hobby and is willing to craft an exceptional product. His games can be relied upon to deliver a superior experience. Even his incomplete/experimental games (Pac-Man 320, PinOut & Crazy Brix) are worth playing.