The water can breach the protective barrier of the shell, allowing fungal spores or bacteria in, but the risk is probably exaggerated. It makes sense that a chemical like chlorine might eat through that barrier more readily. The eggs of some species are more vulnerable to damage from being exposed to water than others. I've had condensation drip on eggs rather often, and haven't lost any as a result, though I have had a mold patch form at least once, where an egg got wet.

I had never considered it before, but now that I think about it, using a dechlorinator that removes chloramines from the water before using it in egg boxes is probably a wise idea.