The problem here would be that Saul and Sukuna’s interests are opposite to each other, ironically. Saul wants to ideally get Sukuna an innocent verdict, but Sukuna wants the death sentence. Assuming Sukuna humors Saul though and let’s him actually argue for him, then I think Saul would know about Judgeman‘s sentences since he has the prep time and the pre-trial talk.
Still though, considering Sukuna’s personality and the fact that the specific charge Hiromi accused him of in the manga was mass murder during the Shibuya Incident, Saul’s fighting an uphill battle. Chapter 244 rather helpfully lays out the possible crimes Sukuna could be accused of during the Shibuya Incident (paraphrased):
1.) Murder of 2 individuals
2.) Murder of 1 individual
3.) Mass Murder (the one that was chosen)
4.) Mass Arson
Now I myself don’t really know any of Saul’s feats, I haven’t gotten around to watching either Breaking Bad or Better Call, but the only strategies I could see him realistically pulling off is to shift the focus to a less severe crime, which would still net Sukuna a guilty verdict (probably the less severe confiscation). The other possibility is that Saul will argue that Yuji was actually the one who committed the crime, which would acquit Sukuna of his charges, but would be (imo) much harder to pull off,