No, there is no power running to the air flow sensor when the control unit isn't powered up. The control unit has to provide power to the air flow sensor for it to operate, so it's dead.
To illustrate this, go out to the car now with it working right, with it running and press down on the air flow sensor plate. The car will die. Then do the same with the fuse pulled out of the OVP. It won't change it at all.
When you adjust the mixture screw, you are making a mechanical adjustment to an electrical part (the air flow sensor). If there is no electricity making it through the sensor you aren't doing anything but screwing it up for whoever is the poor sucker who gets the power eventually flowing through it. Sound familiar?
PS It's kind of like the old trick of unscrewing the cap on the salt shaker as you leave the resturaunt