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First, you need to think of your engine as an air pump. If your 3.4 liter engine had the perfect cylinder heads, perfect camshaft, largest possible valves, perfect intake manifold, at 46 RPM when it makes its maximum power, theoretically it can only flow about 276 CFM of air. I doubt you have these perfect engine components, so the engine flows considerably less, as much as 25% less. Realistically your engine flows more like 250 CFM. It’s not as though you are feeding a big block V8 with a big Holley carburetor. So how much airflow do you really need? In addition, believe it or not, the factory engineers designed your stock air intake including the stock air filter to supply the engine with more than enough air. If the factory engineers wanted to restrict airflow for some strange reason, they would have simply installed a smaller throttle body.
Next, you need to examine the throttle body and the tube that connects it to the air filter housing. I will use my car as an example. The engine is a similar multi port fuel injected, 3.1 liter V6. On this engine, if you measure the diameter of the throttle plate, it is 2.205 inches (56 millimeters). If you measure the diameter if the stock pipe that connects the throttle body to the air filter housing, it is 3 inches, (76 millimeters). Since the stock pipe connecting the throttle body to the air filter is already nearly 50% larger than the throttle plate, adding an even larger pipe will not flow any more air than can already pass through the throttle bore. No real improvements here unless you also add a larger throttle body and enlarge the throttle opening in the intake manifold.
NOTE: The stock 56mm throttle body on my 3.1 flows 345 CFM that is already much more air than this engine can use. Adding a larger throttle body would give absolutely no improvements to my engine.
If you examine the stock air filter housing you will see that it draws its air from an opening in the radiator core support, drawing air from in front of the engine compartment. This air is already relatively cool. No gains found here.
The name “Cold Air Intake” is very misleading. On a cold air intake, even if it has some kind of intercooler, it will NOT cool the air any cooler than the ambient outside air temperature. Also, consider that the air passes quickly between the air filter and the throttle body, too quickly to absorb any significant amount of heat. With a V8 engine, you gain about 1 horsepower for every 10 degrees Fahrenheit drop in temperature. Therefore, even if you could drop the incoming air 50 degrees, you gain a measly 5 horsepower. These gains are proportionately less on smaller 6 cylinder engine. Therefore, they are hardly worth the expense.
Something the cold air intake fans have never explained to me. Your engine is equipped with an EGR (Exhaust Gas Recirculation) valve. This device dumps between 5% to 15% hot exhaust gas from the exhaust manifold directly into the intake manifold. This exhaust gas is over 12 degrees F. A cold air intake can’t make a difference over this extremely hot gas. Your engine is tuned to operate with this so it is not a problem.
The air filter used in the cold air intake is the only component that may give you any real improvement. In general these air filters will flow a little more air than the stock paper disposable element, but only if they are routinely cleaned and oiled. If they are allowed to get dirty, they will work no better than the stock paper air filter.
With these higher flowing air filters, you don’t notice anything until the engine is in the higher RPM range. No real noticeable difference in normal driving. Your engine when cruising at highway speed only needs about 90 CFM.
Personally, I hate washing and oiling air filters. A messy job. I would stay with the disposable paper air filter for this reason.
Just like the computer chip mod in you other question, I would not waste your money. Consider this. $250 for a computer chip. $250 for a cold air intake. Sell this car and add $5 and you have enough to get a similar Firebird Formula that would have a 5.7L V8. A V8 Formula will be faster and quicker than your 6 banger base model could ever hope to be.