Take two computers with exactly the same hardware apart from the coolers. Other has random stock cooler with crap fan, let's call this setup A. The other has top of the line water cooler, let's call this B.
Now if we don't count in the power drawn by the different cooling systems we can agree that both setups with the same hardware consume the same amount of power. If the example A is using 100 watts of energy on it's CPU per second we can also agree that this energy after turned in to heat must be moved away from the CPU area to keep it's temperature stable (this is assuming that the cooler can actually achieve this). Now regardless of the CPU temperature all that 100 watts of energy must be moved away because if let's say only 95 watts was exhausted it would mean that 5 watts of that energy would be stored somewhere inside the CPU every second and the CPU temperature would keep rising linearly higher and higher. Because it's staying stable at the same temperature we must agree that the cooler is actually getting all that 100 watts out.
Comparing this to the example B we should also be able to work out that because it's CPU temperature is also staying stable (albeit at lower point) we must agree that it's also getting rid off all that 100 watts of energy. Now if your hypothesis of drawing more heat out would be correct it would mean that the cooler must be able to transfer more then 100 watts which is impossible given the stable power consumption of the CPU. If this was happening it would actually mean that the CPU temperature would start falling linearly.
If we can agree that all this is true it's obvious that the same amount of heat must be transferred in to the room air eventually. Only defining difference is the time it takes for example A to start transferring as much heat to the room as example B. In the example A there's more resistance in the heatsink material so it takes more time to move the energy from the CPU to the air. Now because there's more resistance it means that in the example A the CPU temperature starts rising to a certain point until it stabilizes and stays there. This time "X" it takes to do this is longer then in example B. When this time has passed and both examples have their CPU temperatures stable both systems will be outputting as much heat. Very simply put it's only this "overhead" that is the difference between water and air. It is true that the example A has more energy temporarily stored inside it's system and hence the higher temperature but the amount of heat put out per second is the same in both cases.
If you want to look at more of the factors included you also need to account in the fact that water coolers are also most of the time exhausting the hot air straight in the room air, whereas something like stock cooler would exhaust inside the case, meaning that this introduces addition overhead when everything else inside your computer has to heat up before the heat can be transferred onward.
When you start including additional stuff like airflow patterns and fan setups it gets extremely complicated to calculate exactly how must faster the room heats up to it's peak temperature but all things considered that temperature will be exactly the same once certain amount of time has passed.