To clarify, after the upgrade, the documents are left in an upgraded version of the Web Storage System database that is compatible with Windows 2003 Server and SPS 2003. The upgrade is an "in-place" upgrade. The existing SPS2001 version of the Web Storage System won't run/is not supported on Windows 2003 Server.
If you use categories in SPS2001, you'll need to have run the SPS2003 upgrade process to have the new MS Document Library Migrations (SPOUT/SPIN) tools "do the right thing" with categories. More news on this in a couple weeks.