They will last longer in the fridge, but there is little sense in leaving them unwashed if you are going to refrigerate them, you just increase the risk of salmonella getting into the eggs for the reasons I explained. The conventional wisdom I mentioned probably dates back to the days of the ice box which have rather high humidity levels due to the massive block of ice slowly melting, in a modern fridge this is not as big of an issue but humidity levels in the fridge can be quite high, depends on what food you have in there.

I can not provide a source off the top of my head, been a few years since I went through my egg curiosity phase. But it is a simple experiment, take an egg out of the fridge on a hot humid day, you will see water condense on them, and if you let it sit you will see that water absorb in, it will disappear faster than evaporation could explain. This will be easiest to see on a washed egg since the bloom on an unwashed egg helps some, but the bloom is never perfect and each time water condenses on the egg it damages the bloom.

I know fridges certainly used to have those egg compartment things in the doors, but never saw anyone actually use them - tends to be the cardboard egg box is in the fridge, this would probably absorb any extra moisture.