Admin Tools never sends any information about your site to the CoreSums service. The only network request it makes is a standard HTTP download of a public checksums file for your Joomla version — no different from visiting a page on a website. No file paths, file contents, site URL, configuration data, user data, or any other site-specific information is transmitted. The service cannot identify your site.
The checksums files are hosted by default at https://getpanopticon.com/checksums. If you have stricter privacy requirements or operate an air-gapped network, you can run your own CoreSums service on your own hardware and point Admin Tools at it using the CoreSums service URL option in the component Options page. The service software is open source and available at https://github.com/akeeba/coresums.