Hi,
I'm new to PlayOnLinux and really don't have much Wine experience either. In any case, the concept is awesome, so I'm submitting this to help you iron out the details.
I just installed Zorin 64-bit, an Ubuntu-based distro, and attempted to install StarCraft 2. I downloaded the setup file from battle.net and pointed PlayOnLinux to use it. It launched great and began installing. A minor issue I noticed was that the installer had a black box around it. It probably should've been transparent however wasn't. In any case, Starcraft 2's updater finished installing the game, yet PlayOnLinux claimed it was still installing. I left it sit for some time with no change.
I attempted to launch the game, which was somewhat successful however there were various issues. One (R6034) was resolved with the command:
echo 0|sudo tee /proc/sys/kernel/yama/ptrace_scope
To launch and play the game, I was clicking install and pointing PlayOnLinux to the Setup file. It would load the launcher, which allowed me to click Play. The background images in-game were just black. Nothing to show, but otherwise appeared to function properly.
When I manually created a shortcut to the executable (which does not launch the game at all), I get the following from the Debug link:
[12/09/12 19:42:44] - Running wine-1.5.10 SC2.exe (Working directory : /home/jason/.PlayOnLinux/wineprefix/SC2_WoL/drive_c/Program Files/StarCraft II/Versions/Base23260)
err:module:import_dll Library icuuc44.dll (which is needed by L"C:\\\\Program Files\\\\StarCraft II\\\\Versions\\\\Base23260\\\\SC2.exe") not found
err:module:import_dll Library icuin44.dll (which is needed by L"C:\\\\Program Files\\\\StarCraft II\\\\Versions\\\\Base23260\\\\SC2.exe") not found
err:module:import_dll Library fmodex_4_28_09.dll (which is needed by L"C:\\\\Program Files\\\\StarCraft II\\\\Versions\\\\Base23260\\\\SC2.exe") not found
err:module:import_dll Library d3dx11_42.dll (which is needed by L"C:\\\\Program Files\\\\StarCraft II\\\\Versions\\\\Base23260\\\\SC2.exe") not found
err:module:LdrInitializeThunk Main exe initialization for L"C:\\\\Program Files\\\\StarCraft II\\\\Versions\\\\Base23260\\\\SC2.exe" failed, status c0000135
Thanks again!