I have always taken the position that global templates (and workgroup templates) should be located on each computer and updates pushed as a part of network login. This should cut down on network traffic and allow for work being done on laptops and off-site. It also makes it much easier to update the templates. (The master copies of the templates are on the network, just not used by Word through the network.)

If a global template has the Style copy routine as part of an AutoExec, it should run each time Word is loaded. If you need to push into existing documents as well as into the normal template (seems extreme to me) you would need a macro run by the document_open event. Then it would push the styles into the ActiveDocument upon the opening of the document. Depending on the number of styles, this could slow your opening down noticeably.