Hiding the WordPress CMS shouldn’t affect the SEO from your website.
All the main URLs should remain unchanged. Only the media URLs are changed once you change the paths.
Through sitemap.xml Google is informed about the new paths and next time the Google will verify the website it will index the new media paths.
We have tested Hide My WP Ghost on many websites and we noticed even a slight improvement in the loading speed and great results in Google search engine, Bing and Yandex.