It is more complicated than that. As gases cool, their density goes down. So when your turbo spins at a certain speed (governed by your truck computer, which does not know their is a bigger intercooler), it initially generates a certain pressure at the turbine blade. But as that higher pressure gas reaches the intercooler, the cooling makes the gas reduce its pressure. For example, a balloon filled in a warm area will shrink when you bring it into the AC. So, everything kept constant, except that you change the intercooler, you should see lower boost at the same load/rpm condition.
The important thing to note is:
1) The amount of oxygen flowing is the same (turbo doesn't know the difference)
2) The air temp entering the cylinder will be lower
3) The EGT's will be therefore lower (under the same load)
Through programming, you should be able to take advantage of this and if your turbo permits, jam more air in than you would otherwise be able to. That will translate into lower EGT's when towing a heavy load up a big hill, so you probably will be able to take the hill at a higher speed without getting into the danger zone on EGT's.
250F lower? Nice! That is significant, and most guys here know that would be important. Is that what Banks advertises? I thought I heard much lower improvements than that, more like about a 100F drop.