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The ground wire is potentially important, and Ford added it for a reason after a year or two of producing the regulated generators. Resistance in the ground circuit is directly deducted from generator output, and there are a lot of potential problem areas if ground is through the mounting...it has to go through numerous bolts, gaskets, and connections to get back to the ground side of battery. On a restored car, everything is complicated by thick paint, on an unrestored one by rust and dirt.
Adding the ground is a good idea for anything other than detailed correctness. It can run from existing through bolts on older gen or from the dedicated post on newer case back to base of regulator to emulate stock later setup, and this can be improved a bit by adding a jumper form reg base to where battery ground cable bolts to car.