No that is not possible. HTML is not a dynamic language like PHP. The page needs to be PHP to perform these kinds of actions. There are lots of great tutorials on building themes for wordpress.
I would suggest installing Wordpress in a sub-folder, selecting a theme then linking to that from your html site.
yoursite.com/blog/
From that there are ways you can still get the latest posts into your "real" home page, but again, that would need to be php.