You need to configure the webserver so that URL requests for the old pages and for images and CSS/JS are served from the static files and URL requests for the WP pages are served by the wordpress PHP script.
That could be as simple as putting WP in a folder or using extensionless page URLs in WP and retaining whatever extension you currently use for the static pages.
Think about this in terms of requested URLs and not as folders and files inside the server.
I don't see a problem. I'm doing this with a static html site (all files have .htm extension). I've installed WP in a /blog folder I created, and all WP files in in that folder. Everything stays separate from the pre-existing site pages. Even if I had installed WP in the root directory, there probably would not have been a problem, since the file extensions are different--as long as the names of the two CSS style sheet files are different.
You can install WordPress in the webroot and it should ignore existing files. (set up the permalinks however you'd like. the rewrites should ignore an existing file. Make sure this is the case for your server) where you can serve the existing .html files and WordPress side by site.
You can install in a subdirectory, ex. domain.com/blog. Then link as needed into the static site's navigation.
Or you can import the .html pages into WordPress, serving with the same .html extension for the .html *pages* via plugin, adding the blogging functionality. (this if they'd like to manage the whole site from one place. the blog related posts/categories/tags related pages won't necessarily have the .html extension unless you config that way.)
In the first two cases, theme WordPress to match-up with the main site, in the last, it's a theme for everything on the site. Lots of choices for you.