I like a ground wire direct from gen case to reg base (Ford did this after '40) and an extra from that to the bat ground cable. Engine ground path is far too messy, with dirt, paint, rubber, gaskets, etc. offering potential losses everywhere...
The car should run with cable yanked (though this is electrically messy as battery drops out of circuit, not really advisable!) IF engine RPM is high enough...regular idle will be a touch low, and if you choose to try this you need to pull out the throttle button a bit.
There are better tests, with gauges employed or without, including a simple procedure to "full-field" the generator...this one will show if generator is good even if reg is kaput.
I compiled a bunch of Ford and Echlin test information on the charging system over on the HAMB, running tests and tests of the pathways within the gen. I even included the once common, slightly scary, field and armature tests using 110 volts to find potential problems. I also posted the polarizing procedures...you have to research this a bit as half the people you go to for advice will give you the light duty Delco polarizing technique, which is incorrect and potentially destructive on the Ford type circuit...
Will see if I can locate those tests.