I really hate to be the bearer of bad news, but this Macbook Air will run WoW, but it will for the most part be the most choppy experience you could imagine. You’ve got the combination of super thin chassis preventing the CPU from sustaining turbo speeds, the CPU’s base clock is very, very far below minimum spec for the game, you’ve only got 8 GB RAM, which is barely enough to play the game (you’ll hit swap a lot), and you’d be running off integrated graphics.
In a nutshell, that’s the worst possible setup you could use for WoW.
Wine does work in OS X, but you’re much better off just booting into Windows via Boot Camp if you can fit it onto your drive(s). Not sure why you’d need Wine for WoW though since there is a Mac native client.