No, they'd have basically just said exactly what happened - I entered, my mother was trying to drown my fiancée, I stopped her but didn't realise how long I held her underwater for.
You have to think about it from a police/CPS point of view - they can't just prosecute on a 'something about this feels a bit dodgy' charge - you have to have a specific charge/crime so for example, manslaughter AND meet the evidential threshold for that (Homicide: Murder, manslaughter, infanticide and causing or allowing the death or serious injury of a child or vulnerable adult | The Crown Prosecution Service) which is high AND then have a realistic prospect of conviction AND pass the public interest test.
You'd have Daniel with the resources to pay for the best legal representation, able to provide multiple witnesses who would have all said Laura had been acting erratically, hated Cherry, etc., plus evidential proof matching their story (drugs in his system, disruption in the house, Cherry wet with bruises etc.) vs a random police officer with a huge caseload and no personal ties to Laura.
It's not like the police would have just turned up and said 'Ah fair play, sounds legit, well very sorry for your loss,' - very likely Daniel would have been arrested and interviewed, possibly could have even gone to court but found not guilty (albeit I think it more likely charge just got dropped), we just didn't see any of that.
It is ridiculous that he didn't attempt CPR though
(unless he did and that's how there's a second season!)