Testing Disk II without the computer

To my knowledge no.  The drive pulls its power and instructions directly from the computer and controller card.  So without them, It will likely just sit there, even with power.   What I do know is that if there is a problem with 6, the card will work in slots 5 and 7 as well.  It's just that certain programs (like Ghostbusters) are defaulted to 6 and won't load from other slots.  

If you hear the read head knocking at boot then stop, then likely the card and slot are good.  Since it's the card and computer that tells the drive to do that (Apple floppy drives really don't do much without being told to by another device).

If you have another drive, you can try swapping the analog cards between them.  Also, if your drives are numbered, try swapping them on the card, as there is no difference between them (beyond the labels).  Unfortunately, you can't load from drive 2 as the computer will always default to the top connecter on the card.  I don't think it will even look for it unless instructed to by software.  However, one thing you could do is load ADTPro over a serial or cassette port and see if it will recognize the drive attached to the lower connector.  It would be whatever Slot (5, 6, or 7), Disk 2.

As for the motor itself.  Try manually rotating it to see if there is a physical jam.  

The only other thing I can think to do (although I wouldn't recommend it) is to remove the motor and feed 5 or 12 volts (I'd need to look at its specs to know which) directly into it to see if it spins.  Obviously, this is less than ideal, as you're risking damage to the motor if you get the voltage wrong.  

Anyway, good luck to you. Hope some of this helps.  If not, maybe someone has a better solution.