Pretty sure the refrigeration is just for shelf life. Refrigerated eggs are good for months (even though the expiry date might lead you to believe otherwise).
I don't know about non-refrigerated but I would guess they can't be stored as long.
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Denmark - European - refrigerated eggs.
See also: Every other discussion about refrigerated eggs on HN.
As far as I know, once refrigerated, always refrigerated. But if your eggs have never been refrigerated there is no need to.