Inferno is correct here. The intercooler on a forced induction car cools the intake air charge, not the exhaust.
The exhaust gasses come out the engine, spinning the turbo. That spinning of the compressor side is what draws more air in and compresses it. But, when you compress air, it gets hotter. So, the compressed air is sent through an intercooler where it can be cooled down before reaching the intake. Cool, compressed air is more dense with oxygen. And that means more fuel can be added to make power.
So, if we're just talking about the intercooler, no I doubt it will make you fail an emissions test. But, the only reason you would put an intercooler on a car is to be able to add more fuel to the mix to make more power. And, that can cause you to fail. So, the intercooler alone???? No, doubtful it would fail. But, everything else that goes along with putting a bigger intercooler on??? Yes, probably would cause it.
Lets face it, the only reason anyone upgrades the intercooler on a turbo car is because they have enough mods to warrant the need for a bigger one. Thus, you are probably already on your way to failing even before the bigger IC.
Hilg