Can I test if a battery is connected to a circuit?
A current measurement from one of the battery terminals would tell you if something is connected. This could be done with a multi meter or there are many other circuits and devices that can measure current. If the current is flowing into the battery then it is charging. If current is flowing out of the battery, there is something connected to it. If you measure no current, then nothing is on, or connected to it. 


Source: https://www.allaboutcircuits.com/textbook/experiments/chpt-2/ammeter-usage/

You may not be able to tell the difference between an open circuit (if a switch is off) and if there isn't anything connected to it.