Storage tank Cooler Motor vehicle

Good afternoon, I have a theoretical question regarding the cooling system of an excavator (similar to the Japanese cooling system car) Key data: -coolant cooler with cap (lower & higher pressure valve) -storage tank whose position is below the cooler -storage tank has an overflow hose and a hose to the cooler cap (cooler) Is it possible that if the coolant level in the cooler is low (due to air in the cooling system or poor filling) and the pressure rises, so that the pressure relief valve opens in the lid -> air in the hose (because air is located in the top of the collection box) comes in the direction of the storage tank. Then in the hose there would be only air (no more coolant) so that a resuscitation can no longer work and thus no coolant can flow from the storage tank into the cooler? Is this possible in theory or must already lack a lot of coolant in the cooler or is it never possible? the case that in the collection box of the cooler so much air collects in engine operation, because the coolant actually circulates? I hope I understand my special question. I am happy to answer.