Yes it matters, look at the diagram. Of course it matters. The ECU power for a 4 terminal box connects to the ignition switch side (blue in the diagram)
I don't have the engine grounded to the body anywhere. I will be doing that tomorrow. Would not having that grounded and not having the ECM grounded properly cause me to burn them out?.
It sure as hell won't do anything any good. There is a REASON why this stuff has to be grounded. In the case of the regulator and ECU, it's "just as if" there is a wire hooked to that ground. "That wire" has to go to the battery NEG. The only difference is, Ma is using the car body instead of "wire."