I don't think that you'd want to run your entire suite of unit tests. Depending on how large the application and how large the suite of tests, this may become a very expensive part of the installation process. Also, unit tests should functional blocks in isolation, independent of their environment.
What might be more valuable is a collection of tests, packaged as a stand-alone program, that specifically target the aspects of the installation that may be problematic. For example, making sure that registry keys were written to the expected location on a 32-bit vs. 64-bit machine or that a temporary file area is readable/writable.