Once unwashed eggs have been refrigerated, must they remain so?

Question

Other questions on this site have addressed the fact that unwashed eggs do not need refrigeration because they are protected by a "cuticle". Washing removes the cuticle, and therefore washed eggs need to be refrigerated.

If unwashed eggs have already been refrigerated for a few weeks, and are subsequently left out unrefrigerated for a another week or two, is it still safe to use them? That is, does refrigerating the unwashed eggs remove the protection of the cuticle in some way, or otherwise make it dangerous to subsequently leave the eggs unrefrigerated?

Edited to add: Since originally posting this question, I have come across the following claim:

In America, food safety officials emphasize that once eggs have been refrigerated, it is critical they remain that way. A cool egg at room temperature can sweat, facilitating the growth of bacteria that could enter the egg through its porous shell.

From the phrasing of this statement, it's not completely clear to me whether this principle ("once eggs have been refrigerated, it is critical that they remain that way") only applies to washed eggs (the context "in America" suggests that may be the case), or whether it applies to all eggs, whether washed or not.

Answer 1

Based on your edited addition:

A cool egg at room temperature can sweat, facilitating the growth of bacteria that could enter the egg through its porous shell.

it sounds like they are saying:

A cold egg brought into room temperature can have moisture from the air form as condensation on the outside of the shell, and this moisture may ""wash"" parts of the cuticle off, allowing bacteria to penetrate inside through the pores (microscopic holes) that now have no protective barrier (the cuticle) covering the pores.

- my uneducated interpretation and extropolation of what they mean

It sounds like the extent to which this may make eggs unsafe is directly related to the amount of condensation that forms on the outside. Theoretically, eggs could be gradually brought to room temperature, preventing condensation from forming.

Alternatively, the eggs could be put into an airtight container, with the air inside also cold, and it'd be the outside of the container, instead of the eggshells, that'd do the sweating. It is possible that a regular egg carton would form condensation instead of the eggs.

None of this is safe food handling advice, merely me thinking through theoretically what might be going on based on the statements provided.