Does the scale use a momentary push switch to turn it on? If so I've seen similar projects that wire the contacts of a small 5 volt reed relay across the built in switch. Then the micro-controller could power the relay coil momentarily to keep the scale alive. Just a thought.
Your idea of injecting a voltage into the scale does sound like a very hit or miss situation as it's bound to saturate the measurement circuit and cause crazy measurements until it's removed.