It all depends how the intakes tuned. The Mazda 3 and Mazda 6 have extremely sensitive sensors, and if the fuel trims are even slightly off (as little as 7%) it throws a check engine light.
AEM and Injen had a HUGE amount of trouble with the mazda 6 and check engine lights...more then 75% of CAI/SRS owners got check engine lights...regardless of how many times they tried to redesign the intakes.
Injen eventually just gave up, and released their original intake as a "race part" with a cel warning. AEM decided to just ignore the problem, since only around 40% of the AEM owners had cel's, and it was found to be insignificant enough that they could deal with the backflash. (Aka would have cost more money to redesign the pipe then to just ignore and get some bad press).
With that in mind, the AEM for the 6i (same engine as 3s) gets an 11.9 hp peak gain, and a 9.7 hp peak torque gain...so those gains are still possible with the 3, the manufacturers just don't want to deal with the whole check engine light fiasco again, and are keeping the trims very close.
(A majority of power from an intake comes from the adjustment of the fuel trims (leaning out the A/F mixture) by using a larger diameter pipe then stock).
CP-E has said they are willing to make an intake for the Mazda 3s, which will use an additional MAF customizer to allow the use of a larger pipe without throwing any check engine lights, as well as a programmable fuel map. Its not yet available though.
http://www.cp-e.com
Remember that there are other ways to speed up a car other then engine mods. Reducing the unsprung weight (wheels/tires) below stock weight, will increase acceleration, decrease braking distance, and increase handling response.
Conversely going with heavier wheels then stock (chromed for example) will result in the opposite effect. Reduced acceleration, increased braking distance, reduced handling response.
Here's a neat formula for calculating the effect of wheel and tire weight on a car's performance.
http://www.mazda6tech.com/files/rotational.xls
And the corresponding article.
http://www.mazda6tech.com/index.php?option=content&task=view&id=16&Itemid=32
Generally a single lb of wheel weight, can usually equal as much as 25 lbs of static weight, if not more.
Remember 100 lbs = 0.1 seconds in the 1/4, or 15 hp.
