If it were a simple matter of Style definitions, and the documents based on the template had the 'automatically update styles at open' option checked, the answer would be Yes. For actual content, the answer is no - and that's probably a good thing. After all, in a business environment, you wouldn't want to have an old document you need recourse to for legal proceedings or a tax audit, for example, to have its content being updated with, say, a new letterhead and today's date. Furthermore, templates don't keep track of the documents created from them, so processing any such change would require a macro that either:
a) runs each time a document based on it is opened; or
b) after the template is updated, goes through all files on your system to check whether they're based on that template and, if so, update them.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]