I'm aware of this post but what I would like is to configure the software center to install software in
~/local/ for example, not to modify the system's policy about who's allowed to install packages... Is it possible? (on LTS 12.04)
No, this is not possible. You cannot install the pre-built binaries in a location other than the one where they were intended to be installed.
Many packages, and other parts of the system, depend on certain files being in certain locations, for things to work properly. In some cases, when applications are compiled into binaries, they have certain paths compiled in, where they may expect certain other files to be. Those files must be in that location for the application to work properly.