In the case of the unusual castile recipe, yes, there is excess lye to neutralize and it appears that the excess water in this soap moves at least some of the excess lye to the surface where it is neutralized with CO2. Ash formation is proof that this is happening. I was doing some thinking and calculations this morning, and I'm not sure just the formation of soda ash is the whole story. If ash formation is the only thing that is neutralizing the excess lye, the soap should be covered in mounds of soda ash. No one who has made this recipe, including me, is finding this to be the case. Not having a chem lab to study this, I'm not sure exactly what else is going on, but despite my ignorance of the reasons, it's clear the soap is becoming considerably less lye heavy as time goes on. AnnaMarie's experience shows the soap eventually becomes mild and skin safe, given time.
In the case of a properly-made soap that is lye neutral or superfatted, it's a little different. Taken as a whole, no, the soap cannot not be lye heavy. That said, there can be localized areas of higher alkalinity within the soap, especially when the soap is young. For example, the bottom of a soap can have higher alkalinity than the top, based on experiments by Kevin Dunn (see his book Scientific Soapmaking) and from information I've gleaned from threads in this forum. I suppose a person could think of that as being a teeny bit lye heavy, although the chemist in me has problems with that -- I just view this localized lye-heaviness as a chemical reaction that is still in process rather than an end result.
Also, soap has a crystalline structure that gradually develops during cure. The crystal structure, being formed of soap molecules, is chemically neutral, but the spaces between the crystals are filled with a water-based liquid that is alkaline. Some of the alkalinity in this liquid is a natural consequence of soap being soap, and some could be excess alkalinity that will continue to react and neutralize during cure. The development of the crystalline structure, the entrapment of liquid within this structure, and ongoing but slow chemical reactions are also part of the increased mildness of soap during cure -- cure is not just about evaporating water.
I think a big part of what I'm learning from the lye-heavy castile and from my recent reading about the chemistry of soap is this -- The cure time is every bit as important as the initial saponification. My "normal" soaps are teaching me this too, but the effect is much more subtle than the lye-heavy castile, so it's easier to overlook or downplay.
I wish I had a better answer for you, but this is the best I can offer.