I don't think so, but easy to check. Pull both field wires off the alternator and check for continuity to ground at each field terminal on the alternator.
Or just unplug the green wire going to the alternator... Leave the blue wire connected... Does it stop charging? If it does the alternator isn't the problem...
Next plug the green wire into the alternator & disconnect the plug on the regulator... Does it charge now? Then the green wire between the alternator & regulator is shorted to ground... If not the problem is further up the line...
As mentioned the regulator meeds a good ground... But it also needs to see full charging voltage on the blue wire, thats the voltage regulators reference voltage... If it only sees 10v on the blue wire it's gonna ground the green wire causing the alternator to charge...