Probably this could be reduced to about half size by removing parts that are not needed, but I guess it would not change things significantly.
Running Slicer from a shared network drive would have many advantages (for example, it would be much easier to handle automatic updates), but it would be very bad if users would need to download the viewer from scratch for viewing data.
A good solution could be to install just a launcher on each computer, which would be responsible for automatically copying of Slicer files from the shared folder to a local cache and launch it when needed (no installation is needed, Slicer can run from any writeable folder). The launcher would be a small standalone application (if built with static Qt then it would be a few MB, if built with dynamically-linked Qt then it would be a few ten MB). If someone does not need the 3D viewer then the full Slicer would never be copied to the computer. The launcher could show download progress, handle automatic updates (check if the locally cached version is the same as in the shared folder and offer to upgrade), custom URLs (so that Slicer could be launched from a werb browser) and file associations (e.g., Slicer could be launched when the user wants to open a .dcm, .nrrd, … file).