Many OJS journals do publish articles in HTML format online, many others publish in PDF alternately (or in addition).
At present, the only way to get articles from .doc format to HTML is, as you suggest, to do the conversion manually between the copyediting and the layout steps in the workflow. However, it is possible to use OpenOffice.org and Docvert (http://holloway.co.nz/docvert/
) to convert .doc files (or any other format) to HTML directly for this step.
We have also been working on an online service which will extend this process to automatically convert articles to NLM-XML for use with the upcoming XML rendering plugin for OJS 2.2 -- which will render both HTML and PDF from XML. Although we're not able to release the conversion service yet (it's still in development), you may wish to try Docvert in the meantime.
Hope this helps; I'm happy to answer any further questions you may have.
Open Journal Systems Team