Yes, it can if your battery has that setting. At CP Solar, we are very familiar with this design configuration.In most solar battery backup solutions, grid is used as a backup source of power. During the day the solar PV inverter powers the loads and excess power goes to the batteries, when the loads’ power demand goes down, all the power available from solar will be used to charge the batteries and when there is less power from the solar e.g. during cloudy days and batteries have low state of charge (SOC) the inverters then charges the batteries from the grid. During days when batteries were fully charged, batteries will be powering the loads during morning hours before the sun rises.