Turbos are all about getting more air into the engine at a faster rate.
An induction kit helps a turbo engine more than a normally aspirated engine, as any gain in air flow in exaggerated by the turbo. Induction kits also add a bit of noise. I put a Blitz Sonic on my last car and it sounded REALLY loud.
Obviously all that extra gas and combustion needs somewhere to go, so improved exhaust flow also makes more of a difference than a non-turbo engine.
To cap it off, the colder the air that goes in, the more dense it is, and therefore the better the effect. That's why its good to include a bigger intercooler (with water-sprayer if the weather's hot!), and to route air into the induction kit that has not been circulating around the engine bay can help.
So, in really broad terms, if you add an induction kit for better airflow, you will gain 5-10BPH, if you add a bigger intercooler, you will get another 5-10BHP, and if you add a free-flow exhaust (the Cat is the biggest restrictor) you will get another 5-10BHP. On my old Evo, I did all of the above, and bypassing the Cat made the most noticeable difference in power, as the boost came in much earlier and the power band much wider.
There are limits however, and the mixture can get a bit lean in some conditions, which can be bad news, as the temperature increases. To avoid this, you need to get a remap, but I would say it is unlikely to be a major problem, esp if you use hi-octane fuel.
Dave