I understand that the complexes are less soluble than thiosulphate and are thus harder to wash out. So if Suzuki is right, the sulphite does in fact help to wash out the complex (at least the mono one), if not "convert" it. I don't know where Suzuki got that information. Maybe it's in one of the research papers from Kodak in the golden age of black and white.
The other thing that I find interesting is that once the sulphite bath is used, washing can proceed in colder water than would be needed for timely washing without the sulphite bath. This has a practical application for many people whose tap water is rather cool and who don't have a mixer.