Only if it's an actual cold air intake and not a pretty tube with a fancy filter on the end of it that everyone calls a "cold air intake". Even the designs that have a heat shield are complete BS. Think about it- where is the fancy filter getting this "cold air"? From the engine bay right off the side of 500-degree exhaust manifolds and right behind a 200-degree radiator?
The stock setup isolates the air filter from the engine bay heat and ducts in air from outside the engine bay- it IS a "cold air" intake. Yes, the expensive aftermarket ones look cool and can flow a lot of air. But, the stock set up already flows more than what the engine can ingest, it just doesn't look cool. I don't know how much this has been tested or proven, but apparently on the '00-'06 trucks there is some improvement to be had by opening up the hole in the fender to the dirty side of the air box. A proven point of improvement (however minimal) on the NBS and NNBS is the tube between the filter box and throttle body. Replacing this with a smooth tube to get rid of the muffler chambers improves air movement which increases throttle response and gives a slight bump in power in upper RPM. It also increases the intake growl when under load since the mufflers are gone.
So, spend a few hundred on a show piece or just open up the hole in the fender and it's accompanying inlet on the filter box and get an MIT (or fab up something similar) and you'll have the same power results. You'll also have the benefit of being able to use a stock-replacement filter.