I don't know if it's exactly an Official Policy (and can see why it wouldn't be publicly announced), but I gather that Apple will run their diagnostic on even seven-year old Macs (and maybe older) if brought to the Genius Bar. After all, they might get a repair job out of it. Certainly in this case, since the computer is officially supported for the Mojave upgrade, they should check it out if you bring it to them with a complaint.
If your Mac doesn't pass Apple's diagnostic, you will have to get it fixed before Apple will listen to you about the Cannot load 'EFI/Drivers/TestSupport.efi' error. You will then have a choice: whether to have it repaired by Apple, or take it to some other (possibly cheaper) shop. If it is repaired by Apple, and still shows the Cannot load 'EFI/Drivers/TestSupport.efi' error, then you have a case, and can insist on a solution.
Note that it may not show the error, if its logic board has been replaced with one from a computer that has never been upgraded to Mojave (or had the noted Security Updates installed – if indeed they cause the problem). Check to see if the Boot ROM in the replacement logic board has a number below or above 200; it seems like the problem occurs when the number is above 200. To make sure, you can go ahead and install Mojave, and see if it can still run AHT. (You can always downgrade back to an earlier OS, as I did; the Boot ROM will not be reverted to the earlier version, however, so it will still be unable to run AHT, regardless of which OS version is on it.)
If you have the Mac repaired by another shop and it still shows the error (paragraph above also applies), you'll have to get the Genius Bar to run their diagnostic on it again. If it then passes, you'll have a case, and can insist on a solution.
To reiterate (once again): Posting about a problem here in "Apple Community" does not bring the problem to Apple's attention. Apple hosts this forum as a service to its users, a place where they can help each other solve problems. Other than providing moderation, Apple pays no further attention to what goes on here. In fact, a Senior Advisor told me he would lose his job if he paid official attention to this thread. I can understand why, and have no argument with this policy.
However, it means that if anybody here wants a solution to the Cannot load 'EFI/Drivers/TestSupport.efi' error – which can be provided only by Apple – it must be brought to Apple's attention via official channels, i.e. Apple Support and/or a visit to a Genius Bar (or AASP). Since Apple Support will almost certainly tell you to take your Mac to a Genius Bar, you might as well go ahead and do that to begin with.