Well in my case, I had a bad ground when I hooked up a sub in my old car and it killed the battery.
I think what you mean by testing the alt. without taking it off is have the car running and disconnect the battery cable. If it dies, the alt needs to be replaced.
Best website for the z31 is
www.z31.com , you should go there and read and search the message board if you haven't already. Or ask your question there if you want more opinions since this board isn't a leader in z31 information.