I don't think so.
Sodium carbonate can only be produced by the lye reacting with CO2 in the air. If there's no CO2 around, the lye can't react to form sodium carbonate. Soap isn't porous like a sponge, so gases like CO2 are not likely to penetrate into the soap. For that reason, I don't see how CO2 can migrate into the soap structure to react with lye there. IMO, the reaction of lye and CO2 to sodium carbonate is pretty much all on the surface of the soap only. That said, I have no way to test this hypothesis, so this is just my opinion, not fact.
The outside of the soap does show there is a lot of ash (sodium carbonate) that forms. But the total weight of surface ash produced isn't remotely close to the amount that would have to be created to reduce the excess alkalinity in this soap. The amount of excess lye present should make enough ash to make the soaps look as furry as my long-haired rough coat collie.
Normal castiles are very hard soaps -- not sure why you are thinking otherwise on that point. I have to say after some months of using this soap, I honestly don't think the superlye castile is a lot different than regular castile as far as the lather consistency and the gel that forms as the soap hydrates -- the gel is the stuff that people perceive as slimy. I hate to disappoint Anna Marie, but that's pretty much my opinion now.