Alright, first, allow me to say I desire answering this question. Secondly, allow me to in absolute honesty, I can not answer the question. I honestly do not know if cotton, organic or not, expires, goes bad.
I can only say I have had a bunch of organic cotton for three to five years. I have no sense of smell. My wife has not noticed any odor from the cotton in question. It seems to wick and let me vape well enough to suit.
Beyond anecdotal, I have no further answer regarding cotton expiring, going bad. I know if one leaves it exposed, then, yes it is very likely it would spoil, mildew, rot. That's the sum of what I know and can offer. Hope it helps.