Yes of course you can recreate that site using WordPress. You gain the benefit of managing all the pages from the WordPress admin, and gain consistency across all the pages due to the templated nature of WordPress pages.
You can start by finding or creating a very basic theme that mimics the look of the existing site. Then just copy your content into WordPress Pages (copy and paste.) You can even make it look like the pages are HTML by adding the .html extension to your permalink structure. You can redirect traffic to your old pages to the new pages, if the names are different.
So long at the host that hosts www.eddaconsult.se supports PHP 5.2.4 and MySQL 5.0, you can run WordPress without a problem. Here are the requirements for WordPress version 3.2.
Without a doubt, you can do this project with WordPress.