To answer this person questions as some others might find this useful.
If I read your post correctly - hopefully you have not purchased the TRD S/C unit yet or do not have a 2005+ Corolla. Like they mentioned above, it was never designed for the DBW (Drive By Wire) system on the 2005 and 2006 Corolla - only fitment are on the 2003 and 2004 Corollas. There were also ECM syncing issues as well. So an aftermarket ECM (stand alone or piggyback type are required). TRD was supposed to release one for the 2005+ Corollas, but nothing has happened yet - I believe they were working on getting the one for hte Scion tC out in time.
Anyway - if you do manage to get it to fit - the TRD S/C actually sits on the cylinder head. Your intake (the four plastic runners from the throttle body to the cylinder head) is removed and the S/C bolted into its place. You don't have to mess with the exhaust manifold at all for fitment. But you can get a high flow exhaust system (header, high flow cat, mandrel bends, bigger tubing, high flow muffler, etc.) But the TRD S/C was designed for the stock exhaust system - unless your modding the supercharger, you don't need to spend the extra money on the exhaust right away.
TRD does not recommend running any aftermarket intake, especially CAI (Cold Air Intakes), while running the S/C. More for warrantee reasons (possible engine damage). The reason is that there is a chance of hydrolocking the engine and S/C if the filter end gets immersing in water. Also they worry about excessive amounts of debris that may get past the high flow filters on aftermarket intakes may damage the bearings inside the S/C case body.
Can you do it anyway - sure. You need to make sure that you are able to do it first with the correct parts - namely fuel computer, injectors, tune, and cooling.
You have to run something like an E-Manage. Basically it is a "piggyback" programmable fuel management unit that intercepts signals to and from the original ECM - you have to load "fuel and timing maps" to get it work correctly - generally have to take it into a tuning shop to do that, or do it yourself with a computer and a wideband O2 sensor (good thing to have) and turn it while driving (not recommended) with some street tuned base maps avaialbe online at different forums. Also premium fuel is a must, water or alcohol injection is highly recommended (a must if you run an aftermarket intake). Since there is no intercooler for the TRD S/C - you have to run a misting system to bring down the intake temps. Will go a long way to reducing detonation. Injector choices and sparkplugs are very important - too big or too small of an injector and you run into a tuning nightmare. RC Engineering and Power Enterprises are two companies that people like to talk about for injectors - make sure you size them correctly to your application and make sure the impedance is correct. Otherwise you'll have to run a resistor box and run into its own little issues. You have to make sure that the plugs can run with boost (need colder plugs - about two heat ranges cooler, minimum one heat range cooler). Don't use fancy platinum plugs (read Bosch +4) or Iridiums for that matter - plain copper plugs first - then once it gets tuned, plain platinum or Iridium plugs (not the fine wire ones). You also have to close up the gap a few throusands (From 0.044 inch to 0.035 is a good start). Fuel pump has to be up to the task - upgraded fuel pump (Walboro or similar) is a must. If you lean out when the boost is up - the engine will go soon after.