Yes, Hide My WP Ghost plugin works with SiteGround host.
As SiteGround is a combination of Nginx & Apache, the rules will be added in the .htaccess file and processed by SiteGround.
SiteGround Caching Compatibility
However, to hide the WordPress common paths to files like CSS, JS, TXT, and HTML, you need to switch off the Nginx caching option from SiteGroung website panel.
This will not affect the website speed but it will improve the security on your website especially if you’re using 7G firewall from Hide My WP Ghost
Change File Permission
To change the File Permission and protect wp-config.php to 640, go to your SiteGround panel and access Website Tools > Site > File manager and right-click on wp-config.php file. Click to change the permissions and unselect Read All.
Change MySQL User Permission
To change the User Permission in MySQL and protect the DB access, go to your SiteGround panel, access Website Tools > MySQL, and click on the user database connection. Click on the Manage Access icon in the popup window.
Select the custom access to MySQL and choose the required access for WordPress plugins like in the image below:
After you install and configure the Hide My WP Ghost on your SiteGroung website. Run a Security Check and see if the changed you made are correct.