Yes you can do it, but depending on your set up this will be achieved in a variety of ways. For example if you are running a theme they often have a template type that is linked to a blog style page. You would create another page and select Blog from the template type. This would then list a page that picks up all of the posts in a certain category.
Wordpress retains all the same functionality of running a blog even if you treat it like a non-blog website. The structure of posts and archive pages is really all you are looking to display instead of static pages. Sorry to be a bit vague but the set up does vary.