Well, your analysis is logical enough. However, engines are equipped with after-treatment devices that allow harmful emissions to be converted into those not harmful before getting into the atmosphere. Besides that, we need to maintain a constant air-fuel ratio, so when supercharger kicks in immediately it majorly allows more fuel to be induced since there's more air to cater for them. This also increases the chances of having some unburnt fuel or incomplete combustion but that is secondary.
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Yeah.. You get my logic.