The login process is carried out even if safe mode is enabled.
However, if the Page is not crawled after login when Safe Mode is enabled, it is possible that the login process has been determined to be a Safe Mode restricting function.
If you also want the Page to be crawled after login, disable Safe Mode.
Also, if you want to restrain processing such as queries while Safe Mode is disabled, please refer to the following FAQ article and use the exclusion settings in the "Crawl/Scan Target Settings" section.
https://www.aeyescan.help/hc/ja/articles/37804931815193