Yes, sure. Just run them.. Most programs are OK with their registry entries being missing and will fill in the defaults.
If you have some progs that do mind about the registry, then (re)install them in 2003 and specify their location on the XP partition.
Mind you, there may be some (old) things that use their own configuration files in their installation directory. If these config files contain path information or suchlike that could conflict between XP and 2k3, then you may have some problems.