Hey There,
The Under Construction is a WordPress plugin and needs WordPress to be able to function. If you remove index.php, then WordPress will not be able to run in your site. If you need to load an html file as your under construction landing page while you are developing your site, please use a different 3rd party plugin that allows you to insert html code as your under construction page. Perhaps, this plugin could help: https://wordpress.org/plugins/coming-soon/
Now if you would want to insist of using the index.html, you should have have installed your WordPress installation in a different folder. For example, your domain is http://example.com/, you can add index.html in the root directory and install Wordpress in wp
folder. You may then access WP in http://example.com/wp/
Hope this helps.