A good question. I have no idea yet, but my first hunch would be: no.
It depends on what Apple installs...
It may be everything gets installed, so yes, it will boot on any Mac that supports OS 11.
Or, based on hardware validation, only the platform-specific pieces are installed.
In bygone days, in a similar situation (booting to hardware different than that used for original install), if the OS did not boot, often one could do one of the following to resolve from the newer hardware:
- Run the latest OS Combo updater (typically the same version and the installed OS), and it would install/fix/replace anything missing.
- Run a full OS install—without erasing the drive—to install/fix/replace anything missing, leaving all user data, preferences, settings, in place.
Based on that history, I would be sure to clone the OS before proceeding, to be sure one could roll back...and then plug in and try to boot. If booting does not work, try step 1, and then if no luck, try step 2.
With a good clone virtually no risk of getting stuck with non-booting wonky OS.
As an alternative, one could do a TM backup too, and then use the Migration assistant to migrate/update the OS on the Mini, and then eventually clone that to the external....assuming there is enough space on the internal drive.