Low Voltage Battery Disconnect, 20A, 12V/24V Auto Detect

Can three parallel connected 12 v agm batteries be connected to the low voltage disconnect?

Is there any circuitry to protect against relay chatter?

is this even worth it for 1amp device running over night? is this going to add .03a or .003a always or only when current passing through?

Isn't 12.1v too low to turn off my radios in my truck sooner than later? How long would they remain on? Does it matter for a car battery?