Yes, the radiator can pull coolant from the reservoir in a properly functioning engine cooling system. The purpose of the coolant reservoir is to provide a place for excess coolant to go as the engine heats up and the coolant expands. As the engine cools down, the coolant contracts and is drawn back into the radiator from the reservoir.

When the engine is running and the coolant temperature rises, the thermostat opens and allows coolant to flow through the engine and into the radiator. As the coolant circulates through the radiator, it is cooled by the air passing through the fins of the radiator. This cooler coolant is then pumped back into the engine to absorb more heat and the cycle continues.
As the coolant expands in the engine, it flows into the coolant reservoir. When the engine cools down, the coolant contracts and is drawn back into the radiator from the reservoir. This process is called thermal expansion and contraction.
The coolant reservoir is designed to maintain a certain level of coolant in the system, so that there is always enough coolant to circulate through the engine and radiator. The level of coolant in the reservoir should be checked regularly and topped up as needed.
If the radiator is not pulling coolant from the reservoir, it may be a sign of a problem with the cooling system. This could be due to a malfunctioning thermostat, a blocked radiator or coolant passages in the engine, a leaking head gasket, or a damaged water pump, among other issues.
In conclusion, the radiator can and should pull coolant from the reservoir in a properly functioning engine cooling system. This process helps to maintain the correct level of coolant in the system and prevent overheating. If the radiator is not pulling coolant from the reservoir, it may be a sign of a problem with the cooling system that should be addressed by a qualified mechanic.