There is always more raw water available than the engine's cooling system can use. I think the "no water will exit" is referring to the engine's cooling water not flowing into the exhaust until the thermostat opens. There will always be raw water bypassing the engine's cooling system and going straight to the exhaust. How much bypass is determined by the demands of the engine's cooling system as thermo opens up. The #12 thermo housing from pic#2 is quite a sophisticated traffic director, keeping the available raw water and engine demand cooling water flow balanced. So pretty sure water will begin flowing out the transom well before the thermo opens. The first stuff that comes out will be what had not drained out of the exhaust manifolds and exhaust tube. Hope this is relevant to the question.
