I think there is a slight lack of education on your behalf.
S3 engines are petrol through and through.
Petrol engines have CAT's because they are measured against this when produced as at the moment HC's, NOX, and CO2.
Diesels are smoke tested as they are not measured in other ways at the moment, although visually there should not be any "heavy" smoke and aromatics should be low.
As has been mentioned they are included on cars as they do a really good job at scrubbing emissions and result in a lower tax banding for the vehicle/owner and an incentive for the manufacturer.