No version of Office "builds on" another, but upgrade editions do require
that a previous edition be installed (or at least that you have the
installation media handy) in order to verify that you have a previous
version. Once Office 2003 is installed, then you can certainly uninstall
Office 2000, though I'm surprised you didn't just install Office 2003 over
Office 2000. The only thing (that I know of) that you might miss is
Microsoft Photo Editor, but you can reinstall just that from your Office
2000 disks if you have them.