BBC article following reductions in successful suicides
(interestingly it says no reduction in number of overdoses. But we have a pretty good reversal for paracetamol-induced overdose - N-acetyl-Cystine - so they should have a pretty good recovery)
Death from paracetamol overdose is by liver failure, and that takes a week or so to happen, but after the first 24 hours there's not much you can do to prevent it apart from liver transplant.
Paracetamol overdose is a small number of liver transplants in the UK, but a significant number of the 'super urgent' transplants.
Is the attempted-suicide overdose rate in decline? That seems to be the main question as to whether the law helped.