When air is compressed, it heats up, and when air heats up, it expands. so some of the pressure increase from a turbocharger is the result of heating the air before it goes into the engine. in order to increase the power of the engine, the goal is to get more air molecules into the cylinder. this means that if the turbochagder is operating at a boost of 7 psi, the intercooled ststem will put in 7 psi of cooler air, which is denser and contains more air molecules than warmer air.
The turbo provides compressed air that flows to the intercooler, than the air that passes through it chills the air and allows the eninge to burn more fuel and air, by packing more into the existing cylinders.
it's just like nitrous, a cold shot of NO2.
i guess you could try it without an intercooler, but i don't think that is a good idea, your car "might" be fun for a while before something went.