Does calcium carbonate fall into this category?

yes, it does, and much of the ground water in the western part of the US is naturaly very "sour" with calcium carbonate and other alkaline 'salts'

and yes, cod is treated with lye to make lutefish, and so are olives--when the are 'cured' and so is corn to make "hominy" (which is then ground up, dried, and cooked again to make grits!) it sounds strange, but various peoples, in various places in the world, have all learned to use lye to 'cook' or 'cure' foods. most alkaloids compounds form 'salts'-- not common salt, but salts none the less. "saltpeter' is poisonous in all but the smallest quanities, but in small quanities, it cures meat and make sausage (and meat) safe to eat even if it hasn't been refridgerated. and sodium bi-carbonate is 'baking soda' and used as a medicine.

the lye solution is rather mild, (it should be so mild that when tasted on the tip of the tongue, its just has a small bite, according to one recipe i read)
i am facinated by how ancient (and even not so ancient-- just a 150 years ago)people used natural products to do rather advanced chemisty, with out having a clue of why it worked, just knowing it did.

people 'knew' how to make gun powder... use a wooden mortor and pestle and mix together charcoal, (preferable form willow wood) guano and sulfer (or brimestone as it was commonly know) and then when it was as fine as fine could be, add a little water to 'corn' it.

(they didn't know why that worked but it did... turn out willow charcoal tends to be "pitted" and water help bond the guana (nitrate) and sulfur to the wood, so the mixture became a compound..that is bound together, and the seperate components didn't seperate out with time.

salt was also extracted from ashes, and of course potash, is just pot ash-- the potasium was first extracted from ashes!

baking powder, is a rather new "invention" and came directly from experiments with indian cooking with ashes to make corn breads. below the fold, back in the spring of this year, there was a thread on salt (there was one above the fold too, but this was one of Dr Bill's and had a list of salt related works, some of them also realate to ashes.

i rememember reading more about them in "Salt" and will go and see if i can find a link to the book.

EDIT
here is a link to the book on salt,
http://www.saltbook.com/links.php

you can read the first chapter on line, and there are many links to other salt related sites.

my other obsession