I have said this previously. CEL (Check Engine Light) is not due to low battery. You may get other warnings to do with AST, ESC etc. with low battery. But CEL is only set when one of the sensors feeding to the ECU detects a persistent or standing error when the engine is running, hence check engine.
This may well be true - I bow to your superior knowledge - however, a low battery can create fault conditions that will then throw up a CEL . I had a CEL a couple of times and had Alfa Assist out to look at it; he was able to reset the CEL. but the fault code related to failure of the turbo coolant pump and it was subsequently replaced under warranty, at which time they also recharged the battery. Some months later I had a repeat - same problem, same code, Alfa Assist reset the CEL again but this time it came back again almost immediately. Back to the dealer, battery recharged and all well again.
I suspect that there was nothing wrong with the coolant pump in the first place, but it is electrically driven and a low battery maybe causes it to show a fault condition (I'll admit I don't know the detail of how or why - maybe it doesn't run fast enough?).
As you say, low battery doesn't trigger the CEL directly, but other battery-related faults do, so it's a knock-on effect, but all you see (in the absence of a code reader) is the CEL.