Yes, you can. However, in order to generate layout independent content, export to Modifier and apply an XSLT to transform the to HTML. You can set an XSLT on output by using the following command:

http://server:port//document.qxp?XSL=file:myXSLT.xsl.

Background:
In QuarkXPress Server you can export to Modifier (created from a QuarkXPress project or a QuarkCopyDesk article) and then apply an XSLT to transform the Modifier to HTML. You can also export a particular flavor of to upload into a WCM. On the whole, we’ve found that customers prefer this approach to the QuarkXPress export simply because you have some control over the HTML that is created. A standard Web Layout HTML is focused on preserving the layout appearance. It is as a result oriented around using frames to set absolute positioning and images to keep the text typography preserved. Applying an XSLT to Modifier allows the resulting HTML to be different in appearance from the QuarkXPress page, and therefore fits better into the rest of a website.