Will hard boiled eggs absorb salt through the shell? In this America's Test Kitchen video they add salt to the cold water when hard boiling eggs.

Would the salt actually permeate the shell and flavor the egg? That seems unlikely to me and is just a waste of good salt.

(Apart from the salt, that method is not new to me. My old, Mom-gave-it-to-me-when-I-got-my-first-apartment Betty Crocker cookbook has the same instructions.)
Salt or acid is often added to the water when boiling eggs to denature egg whites faster should there be a crack and a leak.

I have not read anything that experiments whether this is effective. It also sounds like "don't wash mushrooms" or "pasta must be cooked in a ton of water" kind of old wives tales.