Can WordPress be installed at the root level, if a homepage called index.php already exists?

In theory, you could rename the file and change the rewrite rule accordingly. Assuming you rename it to wp-index.php, it would look something like this:

<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /wp-index.php [L]
</IfModule>

There are a few references to index.php in the WP source, but they’re almost all either in the admin area and used to detect or direct to the dashboard, or explicitly for servers that don’t fully support mod_rewrite.