Since there hasn't been enough testing I suggest you for the time being to do these steps in order to produce results.
1) Go with a terminal to the destination where Age of Conan has been installed . (Update: probably not necessary in 1.31)
eg. cd "/home/maniac/.wine/ drive_c/Program Files/Funcom/Age of Conan/" and so on
2) wine ConanPatcher.exe
If you want to skip the Launcher, check Katsu Akimoto 's post below in the comments... of course dont forget u have to update the client :P ; Not Tested with wine
If you get errors about DirectX when the patcher starts , download and install it
Update Note: You HAVE to use the directx dlls to native after last tests. Note sure which dll as i used the winetricks script to set all the dlls to native (winetricks d3dx9)
Same procedure with my desktop Linux PC. I got a new prefix tried it without any modification and it couldn't find DirectX in the system. So i i did $ winetricks directx then $ winetricks d3dx9.
Waiting for new test data by users in order to find bugs.
Future test includes installing the game and running it , whereas as now running it from the windows partition