it wont be much smaller. It's not like you have a huge water reservoir to soak all the heat from the engine.
The radiator cannot be integrated with the engine's water radiator, as the engine water will probably be hotter than 80 degrees. The air from the intercooler will be maybe 35 degrees hotter than ambient, and maybe it can be cooled to around 20 degrees above ambient.
These temperatures are way lower than the water temp in the main radiators, so they cannot be integrated.
The intercooler will be smaller than an equivalent air to air intercooler,but the radiator will not necessarily be that small.
Air to air intercooler packaging is much smaller than the total package of an air to water system.
The advantage of the water system is being able to split the system and locate the intercooler in areas that dont recieve airflow. For an F1 car which has such a small volume, it may not make sense, as there aren't much volumes on the car that aren't touch by air.