no not likely the reg has nothing to do with the voltage as long as the key switch is only in the on position. Vehicle running then yes it has to do the tach in supply voltage only. If what you say is right then when you turn the key to the on position and it pops a fuse, it is without a doubt directly shorted to ground somewhere. Disconnect the tach and turn the key on does that fuse blow? start the vehicle up and check voltage of the alt. hook the tach back up does the fuse blow then? if so it's the tach. Disconnect the alt and start the car up does the fuse blow,,,,,,,, you get the idea now,,,, isolate each until the offending item is located then fix JMO
Good luck
racy