People remove their cats on petrol cars and either have a 'friendly' MOTer or just put them back on for the MOT and take them off again. Whether it is a criminal(?) offence to do that or not I am not sure - I think it is one of those grey areas. Presumably the DPF would be the same thing.
Please stop saying "delete"!
If your car is in a state where it would fail an MOT you're driving without a valid MOT and thus driving without insurance AFAIK