The stock airbox on the Corolla is really restrictive. A freer flowing intake and exhaust will definitely bring gains to the Corolla. With a simple tune, you could easily double your gains and get the most potential out of a CAI and exhaust. The only cars where they would lose power with aftermarket intakes are sports oriented cars like an S2000 or GTR because those systems are designed to be high performance in the first place. Here's a video that just goes to show what a simple I/H/E mod can do:
(He has a thread on TN and he states that he made about 9-10hp and that may not sound like much but it definitely shows that they do work.)
And this is a Matrix that has intake and exhaust mods and is tuned as well:
From his description:
Stock 2AZ 130-135WHP
Baseline 154.60HP /153.78lb*ft
"After" OV Tuned ECU ** 168.13WHP / 172.13ft*lbs**