Does turning the air conditioning off when you’re not home save energy?

Air-conditioning not only cools the air, it also cools the solid materials inside the house. That acts as a bank of thermal inertia. If you keep switching off the air-con, those materials never get to reach a cool temperature too.

For those who advocate turning off the air-con during the day, tell me, do you switch off your refrigerator during the day too?

Much better to have the the air-con 'idling' all the time rather than working either 'flat-out' or 'off'. The same arguments also apply to heating as for cooling.

Read up on duty-cycles.

In stable state, your AC move as much heat out of your house as flows into it because of the heat difference between inside your house and outside of it.

The inflow is higher, the higher the temperature difference.

Switch of AC, and the temperature difference goes down, and so does the inflow.

So, if you switch off AC for part of the day, the total daily inflow of heat goes down, and, over the entire day, the amount of heat your AC has to move out goes down, too.

Unless you install a huge AC to bring down the temperature very fast, I don’t see a reason why that wouldn’t lead to lower energy use by your AC.