If they are a skilled company they will be able to recreate the site and its contents using wordpress, keeping the same URLs and headers. However, I seriously question whether this is a good idea. What's wrong with continuing to maintain the current site, and retro-fitting a custom CMS into the HTML pages in phases?
I'd start by setting up handlers to have .html parsed as PHP, and then switch out core repeated blocks in the .html pages with PHP calls. New pages would be handled by using a custom 404 handler or mod_write for non-existent files, so that it would be directed into fully virtual (dynamic) pages.