Um, that's not the regulator- that's the ECU. You really should bolt it back down on rubber mounts.
Yes, although it is kind of a PITA to get there. I ran a ground wire to a relay from the reservoir mount. You will need to remove the paint, so you get a good contact. You could also just obtain a longer piece of wire, a couple of crimp-on fittings and attach the ground to the battery.
Darn, that's why I mentioned what I thought it looked like....so let me see if I have this right. The regulator is actually the thing located between the horns. So what is the ground wire that comes up under the ecu and attaches to one of the ECU mounting bolts.
Umm, put down the screw driver grasshopper.. take deep breath.. what exactly are you trying to do?