Can devices be turned on by solar panel once the battery is depleted?

I have multiple solar powered devices, such as solar path lights, solar step lights, and flood lights with solar panel.My area will be raining for the next week or so, and I am sure the batteries will be depleted running the typical schedule.My question is:Once the devices are off because they won't be charged during the rain, will the devices be turned on automatically by solar power once the sun is out again?Or I will have to charge them individually to a certain percentage, turn them on, and then put them back in the sun?Thanks!