I have a 500VA UPS. In our area power cut is very high. So to run the computer I installed a big battery in my UPS near about 64ah. In the day time the power shut down. So I use the battery. The power comes in the evening time. My question is that can the UPS charge the batter pluged into the power and switch off.

If the UPS is plugged into the wall outlet and the wall outlet has power, most UPSs will charge their internal battery with their power switch off. However there may be a jumper on the rear or in the battery compartment that needs to be connected for the battery to charge as most new units ship with the battery disconnected.