Apologies for the tardiness of this response. Tuesday is Looking After The Grandson Day which is pretty full on while I'm doing it and leaves me totally shattered afterwards!
Okay, from the top (and please excuse me if I ramble at bit)..
Yes. Sodium salts do tend to be water soluble in a way that Magnesium & Calcium salts aren't. However, it's not necessarily going to impact things in this case.
We've already established that there are two parts to an overbased metallic detergent; the organic detergent bit & the mineral carbonate bit. The carbonate bit provides the acid neutralisation capability while the detergent keeps the carbonate in colloidal suspension in the oil.
In the case of overbased Calcium sulphonate (by far & away, the commonest overbased metallic detergent), the organic detergent is Calcium Alkyl Benzene Sulphonate. You can visualise this stuff as having two 'ends'. The Calcium 'end' which is polar & attracted to other Calcium ions (remember in chemistry, 'like likes like') and the Alkyl 'end' (usually linear C18) which is non-polar and highly oleophilic.
Together, the detergent & carbonate form colloidal micelles structures which are not unlike those diagrams they showed you at school of sperm fertilising an egg! This is important because while the anhydrous carbonate micellular core might have a strong affinity for water (especially in the case of sodium) because it's surrounded by loads of alkyl chains, the structure, taken as a whole, is extremely HYDROPHOBIC (this is why detergents are so good at preventing rust)
All commercial oils have to be subjected to & pass the Engine Oil Water Tolerance (EOWT) test. I've never ever seen a Ca or Mg oil fail this test which says how strongly the carbonate cores are protected from water by the surrounding alkyl chains. I've never tested Sodium-based detergents but the very fact that these have been used (by Valvoline) says to me they have been through & passed EOWT.
Let me backtrack a bit. When you make a overbased metallic detergent, you can't simply dump a whole lot of metal carbonate on top of the organic detergent & stir. All you will get is a nasty, powdery & probably very abrasive goo! To make the trick work, you have to form the carbonate 'in situ', at the molecular level, such that the particles of metal carbonate are small enough to be suspended by the detergent. You do this by making a mix of detergent, base oil & basic anhydrous metal oxide (or hydroxide), heating it & blowing carbon dioxide (CO2) through it. As soon as the carbonate forms, it's zapped by detergent molecules and colloidally trapped.
I'm raising this because now the metal carbonate, although technically a 'solid', doesn't have many of the properties of a solid. For example, overbased detergents, if they've been properly made are clear & bright liquids which are totally transparent. This is quite amazing when you realise it might contain say 30% of chalk! This stuff is just not abrasive because metal surfaces only see the outer alkyl chains & not the metal carbonate core
The outer layer of detergent alkyl chains won't prevent the alkaline core from reacting with acids. However, because these reactions occur at the molecular level, and all you're doing is trading one metal salt for another (eg calcium carbonate for calcium nitrate or calcium sulphate), the metal-to-metal 'bridge' remains intact so once formed, the new salt is taken into colloidal suspension.
So in direct answer to Shannow's questions...
The normal rules for aqueous solubility of metal salts doesn't apply here.
The metal salts in detergent always start out in their anhydrous form & won't readily form hydrates because of the hydrophobic nature of the micelle structures.
All fresh oils are tested for water tolerance in the EOWT test. I've never tested a used oil on the EOWT but my guess is that it would pass easily.
Acidic species are locked up in the detergent & should not precipitate even in the presence of water. I may be wrong but I suspect this is as true for Sodium as it is for other metals.
I don't believe some metal salts will be more corrosive than others. All the testing I've ever done confirms that detergents are great preventers of corrosion. In fact I'd go so far as to say that even when the detergent's carbonate core has been fully neutralised, that the resultant 'stuff' still has anti-rust properties.
Hope that helps & again apologies for not answering yesterday.