With CrossOver 11 (which incorporates the latest revision of Wine 1.4-rc??), Anarchy Online is once again mostly working once again. Even the in-game store works now.
The problem is that Anarchy Online switched to "Raw Input" for mouse movement somewhere around version 18.4 and Wine does not currently handle Raw Input (see http://bugs.winehq.org/show_bug.cgi?id=25654 and http://bugs.winehq.org/show_bug.cgi?id=20395). The game is mostly playable except you cannot use the mouse to look or steer. You can use the numberpad to do the same, but the sensitivity is a bit high on my machine.
When Wine finally gets a proper implementation of Raw Input, then Anarchy completely work. In Wine, if this patch is applied to the source, then Anarchy Online completely works, but this patch only really works for Anarchy Online and isn't a proper general solution. There is about a dozen games that suffer this problem per the winebugs report.