Nope. I tried with a phone charger+phone (drawing 400mA or so) and a cooling box (drawing 3-4 ampere), but got no warning...
I got a chinese PCB that I can set to turn ON when the voltage is e.g. 13.8V and OFF when it drops to 12.8V, but it used 20mA in standby. And since I already doubled the standby current with my CEM fan that runs 24/7, I cannot double it again with that gizmo