Properly designed headers and exhaust can boost performance, by allowing more efficient flow of exhaust gases. This improved exhaust efficiency (lower back-pressure) is usually associated with an increase in mass flow
into the engine as well. The air/fuel ratio is constantly optimized by the CPU (when running in closed-loop), so more air moving through the engine typically corresponds to an increased fuel consumption.
That's the price you pay for performance with this type of mod.
As for a CAI, the C7 already has one, and there are plenty of entertaining videos of dyno tests where CAIs do nothing to improve power. Some even dyno the engine with the entire air filtration system removed, with no performance gain, demonstrating that the existing air filtration system is not restricting air flow (and using sufficient cooling air to ensure that intake air temperature is the same between all dyno runs).
But hey, it's your money...
and the placebo effect is very real.
One of the entertaining videos.
This video has strong opinion and adult language - even more entertaining.