Yes and no.
The email you are interested in is sent by the "System - Joomla! Update Notification" plugin shipped with Joomla. It does not allow modifying that URL.
You can, however disable the "System - Joomla! Update Notification" and enable the "System - Admin Tools Joomla! Update Email". Our plugin DOES include the administrator secret URL parameter.
In fact, our "System - Admin Tools Joomla! Update Email" plugin came first by nearly six and a half years and it was originally part of my Akeeba CMS Update component (which was eventually included in Joomla itself as the "Joomla! Update" component you are now using to update Joomla). When finally Joomla was convinced that my plugin does help people get notified about and install new Joomla versions much more efficiently than Twitter and announcements on joomla.org they allowed a simplified version of it to be included in Joomla itself. The obvious problem, of course, is that the terms for including the simplified plugin in Joomla itself is that it should not be tied to any third party extension which is why the "System - Joomla! Update Notification" plugin doesn't include the secret URL parameter and doesn't allow the admin URL to be changed in any way.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
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