The engine has to be running or the ASD relay will not close. Testing for voltage you should not damage anything and yes you can check the heater inside the sensor with the Ohms setting but I don't know what the value would be, but at least you can verify that it is not open. If there is no power on the two heater wires try checking from hot to the frame, then if you see power you'll know it's a bad ground, otherwise it's the hot side. Might be a good idea to verify your engine to frame ground anyway.
Update: Advance Auto offered to warranty exchange the O2 sensor. While I normally don't like throwing parts at a problem this seemed like an easy test for no cost.
At cold the codes were gone. Once I hit operating temp I got the high voltage code from bank 1 sensor 1. So now the heater code is gone but still getting the high voltage.