A family of Microsoft word processing software products for creating web, email, and print documents.
Yes, you can do that.
In Word 2007, 2010, and 2013 (and presumably future versions), AutoText is just one particular gallery within the Building Blocks feature. The last paragraph of this article on the Microsoft Word Blog explains how to set up a shared location on a network server for Building Blocks.
Word will load building blocks from any templates it finds in the local and/or network locations, so you can have multiple templates there. You could have one that's standard and maintained by one person, and one or more that may have entries added by anyone.