No, TextEdit cannot read those. You will need to convert them to .doc files first:
Mac users using Word 2004 who receive a Word 2008 for Mac, (or Word 2007 for Windows) document, will not be able to read this without having the Open XML Converter installed, which can be downloaded from Microsoft.
Go to this page:
and click on the right under Most Popular, 'Open XML File Format Converter for Mac 1.0.2'
This opens a window at the bottom of the page. Scroll that to the bottom and click on English.dmg, and it will download for you as a disk image, which can be installed in the usual way.
After installation you can open and read .xml formatted Word 2008 documents in Word 2004.
Update: This link http://support.microsoft.com/kb/976831 takes you to a newer version 1.1.3 (released Nov 10, 2009).