Greetings from Finland.
I'm running Deepin Linux 12.06 64bit (same as Ubuntu 12.04). I purchased and installed Anno 2070 from Steam. Steam is installed in clean Wine bottle and Wine is version 1.5.15 (CrossOver version is 12.1.0).
Download and install Anno from Steam same way as you would do in Windows.
When Anno is downloaded and installed go to your CrossOver gui, select tab Control Panel and open Wine Configuration. Then add new override for library msvcrt40 (native,builtin).
Now restart Steam and click Play Anno 2070. Now Anno Autopatcher will open and you may see error message about version.txt, just ignore it and press enter. (If you don't see any error messages you will see Play button...click it ;) ) Now Uplay will open (in my computer this takes about 2min for some reason, just be patient) and perform self-update. When update is finished you can login with your Uplay account or you can create new one. When Uplay starts first time your friends list will be blocking the view, restart Uplay and friends list should disappear. Now just click Play button and Anno should start loading (this also takes looong time).
Sometimes when game is loading Uplay crashes suddenly and you will see Program Error window, just don't click the Close button and the game should continue loading normaly.
If you want to Alt+Tab from Anno just configure Anno to windowed mode and it should work.
Hope this helps someone :)