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It depends on the car and the filter. It is not that instant, as it requires the O2 readings to wander significantly in closed loop running. Won't affect idle, WOT or anything else, not unless the discrepancy is so big it throws the long term fuel trim completely out of whack and the car starts to adapt over the next few hundred miles.
And even then, with the limited fidelity of narrowband O2 sensors that come on most cars as stock, sometimes, the car can't adapt. Or, it maladapts, which is how the Mazdaspeed brand CAI causes CELs on the Mazdaspeed3 and 6, and how certain cheap aftermarket filters with MAF adapters cause Subarus to blow up.
The better modern brand name filters and CAIs are tested extensively to ensure they don't cause the LTFTs to wander, even when they lean out the intake charge.
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