Question about Insurance Premium calculations

I've been told that Insurance companies don't actually factor in demerit points when re-assessing premiums. If this is the case, is there very much reason trying to fight to have them lowered (and incurring legal expense) if a conviction is the only thing that matters in the calculation?

Also: if a conviction for "careless driving" is fought and won in court, can it still be used by the insurance company when calculating the premium, if they're already aware of the initial charge?

Just wondering if I should take my lumps (pay the small fee and demerits) or try and negotiate a better deal (I'm going to do this anyways) or take it to court, if its all irrelevant in the end, to the insurance company.