G'day Garey,
Yes you can do exactly what you describe with Alfresco. In fact I think this is a great first step for bringing an existing static site under management in Alfresco - simply grab the content in it's current state, copy it into Alfresco via CIFS, then configure Alfresco to deploy it to a static docroot.
Once you've got that up and running you can start introducing more advanced features as appropriate - workflow, Web Forms, dynamic runtimes etc.
Cheers,
Peter