Yes.
The old way (still works in Visio 2003) is to have a template (vst or vtx)
in a folder (or sub-folder) that is in the templates file path (Tools /
Options - sub location depends on Visio version)
The new, additional, way in Visio 2003 is to use the Visio Publising Tool to
modify a windows installer package (msi)
Also, since Visio 2003, you can import a preview image (CopyPreviewPicture)
to provide a good looking template picture.