Black is not a natural color of akoya, it is died. Always. So what the overtones are depends on the manufacturer. So far, I've found pitch black, silver gray... bluish, greenish... even brownish black akoya. They all all labeled 'black' so the only way to find various overtones seems to be shopping around.
What the natural (untreated) akoya colors are... is a good question! They certainly aren't born pinkish white - or at least not the majority of them. Think greenish, yellowish and grayish white + lots of bleach, some heat, some varnish...=pinkish and silver white. Some of these natural colors are mighty beautiful - I think (the silver and bluish grays, the cream ...), just that much harder to match and sell then the bleached whites with uniformly tinted overtones. Poor akoya! Not saying that most natural colors deserve to be saved for posterity, no way. Especially if the icky ones tend to prevail with pollution, as sometimes implied by reports here and there.
I am not sure if this is what the question was intended to ask though. Is it?
Natural color akoya -
at Joseph Stachura & Co. and
at Pearl Paradise.
I believe that white is a posible natural color, just not common (albino or amelanistic mollusks).
This being said, I am not making a case about treatment here. Just trying to count the options.