Yes no problem with idle at cold start.
I removed the secondary air pump on my E46 M3 back in 2008 without any software reflash and it does throw a code but that's it, didn't feel any difference when starting the car.
The SAP is there only to shoot some air so the cats warm up faster and are more efficient.
When I installed CSL headers last summer on my car, I didn't got a CEL either.
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