Short Answer
No.
The Reason
If you take a look at the .htaccess file in the root of your WordPress installation, you will notice these few lines generated by WordPress ( If you have pretty permalink enabled ):
# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
# END WordPress
Pay attention to line 5. When you make a request to a WordPress website, this rule will send it to index.php. But it appears that you want to eliminate index.php file. Even if you manage to do it via rewrite rules, there would be a million of other requests that are sent to this file by default. Not to mention this file is being used internally by WordPress.
Generally it’s not a good idea to have two CMS or platforms installed into a single directory.
What To Do?
What you can do is, to install your WordPress inside a sub-directory, and then use rewrite rules to eliminate /sub-directory/ from certain pages that you need.