My experience is on 18 wheelers. Without a program to actually check the code, we try a simple check. If the ecm is programmed to shutdown the engine for low coolant and that is what it is doing, if you unplug the sensor the fault will change from "coolant level low" to "voltage low" . The engine will not shutdown for that.
Has anyone checked the actual code? I'm assuming it is level low since the buzzer is going off also. Kind of weird for a wiring problem to give coolant level low code. If no one has read the codes that may help if you are interested in fixing the problem. I prefer to have the sensor working in case of a big leak sometimes you will lose water so fast that the temp sensor will not catch the high temp.
Electrical problems suck though. I see crazy stuff every day. Just when you think something can't happen, it does.