If by DataStream you mean XML file then the answer is yes, as long as we speak about text. Illustrations are a different subject.
The first thing to decide about is network protocol(s) and server. On one hand server should support protocol allowing your OS to incorporate stored documents into your filesystem. In other words, InDesign should allow you to import these remote files directly from the server. SMB, NFS, FTP, SFTP or the like all seem to be reasonable choices, as well as so called internet disks (Dropbox, Google Drive, SparkleShare and similar). On the other hand, authors (copywriters) should be able to put their files on your server. It's up to you to decide how. The same protocols should work as well. Security should be one of the main considerations behind the choice.
The second thing is how to export XML from Word documents or how to transform these documents into XML (docx consists of XML files, but that's another story). There are infinitely many ways to do that, but exporting a document so that the name of each used style would correspond to the name of XML element seems most straightforward. There is an article about exporting Word document as an XML file. It's from 2001, but appears to be still relevant: http://msdn.microsoft.com/en-us/library/office/aa140221%28v=office.10%29.aspx
The last part is how to use XML files in InDesign. The most important thing here is that you can link XML files to InDesign document, the same as you can do with images. When XML file is modified, you are notified about it in Link panel and can update your document to be in-sync with the XML file contents. You can also assign styles to XML elements, so styling can be done in great part automatically. The rest is explained in the fine manual in quite a detail ;}.
Actually, Word documents (and other supported text files) can be linked to InDesign documents too. They are visible in Links panel and InDesign document can automatically update its contents if they are modified. The option for that is in Preferences, inside File handling section. See: How can I localize an InDesign file?