Create hidden wordpress site, keep existing HTML website active

Just as the title suggests:

I have a website that uses HTML5 with some CSS that I would like to be able to run alongside a WordPress installation, however I do not want the WordPress install to be visible to the users who may visit the current page at this time.

After developing the new WordPress site I want to be able to remove the existing HTML pages and redirect the domain to point to the WordPress install — is this possible?