All PCMs have long term and short term fuel trim tables which it adjusts over time while you're driving. If you disconnect the battery or otherwise force the PCM into relearning, you might notice that it runs a bit different for a while as it rebuilds those tables. It's constantly reading the narrowband O2 sensor voltage in closed loop and adjusting the fuel to run at stoichimetric which is 14.7:1 for pump gas. It uses those tables to predict what is needed. Changing the restriction in the system might mean for 20 minutes of driving the PCM is "learning" a change. But when we go into wide open throttle, it kicks out of closed loop (after some time) and moves to the open loop tables and those are static MAP and RPM driven.
I thought LTFT applied to open loop. Apparently that's true for many cars, but not Chryslers.
A CAI really doesn't seem to have any performance effect at all in lower rpms in WOT and I would assume zero effect in part throttle into even higher rpms. No change in MAP, no change in rpm = no change in the PCM commands to the spark or fuel. So there is really nothing to learn or unlearn. Maybe up in the 4000rpm range you start to see some part throttle situations where the CAI is flowing better than stock and you see less pressure dip in the intake. Maybe it's a bit more efficient in certain situations.
A CAI makes a small peak change that is measurable but not really significantly noticeable. Off-peak the difference only gets smaller.
The main noticeable difference is sound. Like if your girl gains 3 pounds and asks if she's fat now. Yes you can reliably measure the difference. No you can't really see it, and you wouldn't be able to tell anything changed if she wasn't making new noises now.
It's kinda like the placebo effect of a 62mm throttle body. The stock motor can't pull more air into the cyclinder than the stock throttle body supplies, so it's not a restriction. But the larger bore of a 62mm throttle body means that the throttle cracks open more with less push of the pedal, making you "think" the throttle is sharper or more responsive. On the dyno they're ineffective on a stock 4.0L at wide open throttle.
"The stock motor can't pull more air into the cylinder than the stock throttle body supplies, so it's not a restriction" - This is bro science and goes against the basic principles of hot rodding and fluid dynamics. It's wrong, but practically speaking it's right. Like getting a 1% raise, yes it makes a difference but no it's not significant, practically.