So I'm curious did the PROCESSOR TEST actually do anything?
AFAIR it's exactly the same as loaded from the diagnostics disk. It runs a bunch of subroutines, each testing several instructions. All NMOS instructions are tested, none of the CMOS additions (*1).
One would think that if the computer got far enough to boot the diagnostics and display the screen, then the CPU MUST be OK, right
For one, there isn't many code until the card gets booted by the Autostart ROM - and not all instructions are used until then. I wouldn't wonder if it's less than 30%. Keep in mind, there are ~160 different opcodes - plus decimal mode for all ADC/SBC to be testet.
Or is there something that it attempted to do to validate that the CPU was indeed OK?
As said, it calls up all instructions and verifies the results.
*1 - The original Apple II, II+ and early IIe had an NMOS 6502, while the later IIe and all IIc used a CMOS 65C02 which offered additional instructions. AFAIK the CPU tests have never been extended to cover the new instructions.