If the cooking water isn't discarded, I don't expect baking soda to be helpful other than in neutralizing the acidity, which prevents it from reacting with teeth. Not sure what is the purpose of adding baking soda to boiling water, it must not change the solubility of oxalic acid in a favorable way, perhaps it's to rupture plant cells so that more is released?
To be effective, the reactant/neutralizer has to make the molecule poorly soluble/absorbable. The goal is to form such complex prior to uptake so that this doesn't happen in organs. As far as I know, baking soda can't do this, it might even make it worse because once sodium oxalate is absorbed, there's dissociation, the body will have to deal with both; oxalate will be moved towards excretion through kidneys while extra sodium in the blood may lead to alkalinization for lacking chloride and having to maintain ion balance through the increase of 'hydrogen carbonate' (bicarbonate). This tends to the formation of insoluble salts in kidneys, something that acidification opposes in most cases. But the process is mitigated since alkalinization keeps minerals in bones.