The relay does not engadge, so it will not help to give direct earth to the fan as far as I understand.
BUT, we might have misread the wiring diagram and measured the "blue/yellow cable" (from ECU) into the relay box against earth/ground. I now may rethink - that the blue/yellow cable might give "earth" from the ECU to the relay control. If that is the case, we have to look at the + side of the control signal to the relay...