I guess the same thing would happen if she clipped the sensor wires?
If she clipped the wires, it would trigger the alarm if armed, or ding the console if not armed but in Run2 mode, and in all cases it would light the LED.
Having said that, if you give the wires enough exposed room to play with (from giving it more length), one could easily short it out, thus disabling the door switch.
If she did remove the batteries, she would have to reset and re-install all the sensors to hide what she did. As
Charles alluded to, you may not catch her in the act, but you would definitely know what happened.
If you're handy with doing a modification, you could wire a Normally Closed switch in series with the door sensor switch and position inside the DS10A's battery door so that it becomes a tamper-proof switch. Of course it would have to me reasonably small to fit, and positioned stable enough to not be the cause of a false alarm. One idea might be to wire-up and attach two small pieces of metal, one on the top of the door and the other on the base where the door meets it when closed.