I installed the deb package from playonlinux (4.0.12) (not from the repositories, as there is still version 3.8) and then installed starcraft2. The installation worked fine.
However, if I start it, I a window pops up with the error "DirectX could not be initialised ...". I used the nvdidia-driver 280.13 which was automatically installed by Ubuntu through the restricted drivers menu.
I think under Ubuntu 11.04 everything worked without problems.