Yes, all of the Applied Innovations hosting accounts fully support publishing with Microsoft Expression Web. With our hosting accounts you'll be able to publish your site using FTP (the preferred method) or FrontPage Server Extensions (FPSE). It's recommended you publish via FTP and not FPSE, however we do support both methods.
We do not support publishing via WebDAV on shared hosting due to security concerns.
For more details on our expression web hosting plans visit: http://www.appliedi.net/expression-web-hosting/