Do eggshells let flavours pass through during boiling?

Yes, they will taste different. Egg shells are porous in order to provide oxygen to the developing chick. While the egg is still uncooked, it will take on the tastes of outside ingredients fairly easily. As it cooks, the albumin coagulates and forms chains that prevent moisture and vapor exchange, so it becomes resistant to absorbing outside ingredients. As a result, your egg will pick up more curry taste if it is boiled from raw in the curry sauce than if you boil an already-cooked egg in the sauce.

I would say it will.

One of the fixtures of 7-11 stores in Taiwan is a slow cooker with boiled eggs. They add large tea bags to the set of eggs when starting the process and the eggs turn out brown all the way though. Longer cook results in a deeper brown color.

I'll add a picture soon.

The one boiled in curry will taste different. How different will depend on a few factors, time being the main one, temperature, concentration of your curry sauce and its viscosity are other obvious ones. Egg shell is most definitely porous and not just permeable.

There is a lot of misconception about the properties of hard boiled egg white. It may look rubbery and solid, but there is far more water (80% w/w or higher) than protein inside. Thus there is plenty of scope for diffusion into and out of it.

You will most definitely get salt, "protons" (H3O+ or acid) and even bigger molecules diffused into it given time. You can simply put a peeled hard boiled egg on a thin layer of soy-sauce for a hour or more to see how far the colour will travel into the egg white. Even at fair low temperatures in a fridge, the diffusion is unmistakable. This is driven by osmotic pressure, high concentrations of dissolved solids outside and low concentrations inside. If you then put the marinated egg white onto a thin layer of clean water, you will see the water darken as the soy-sauce diffuses out.

The same is true for meat in fact despite claims that marinating is purely a surface treatment and molecules bigger than salt cannot diffuse in. It is only a surface treatment if you are liberal about how deep "surface" is. Similar experiments will confirm that.

A one-dimension Fick's law model does give a reasonable prediction of time required to penetrate a given depth: depth is approximately proportional to the square-root of time. For egg white in the fridge with liquids with high concentrations of dissolved solids like soy-sauce or balsamico or worcester sauce, depth of penetration in centimeters is roughly 0.0004xsqrt(time), time is in seconds. 1 cm takes about an hour. It is a relatively quite a fast process in fact. Obviously, shell-on, the diffusion coefficient will take on a lower overall value, first there is diffusion into the shell, and then from the shell to the white. Different marinades (and whatever your are marinating) will have different coefficients at different temperatures. These values are very easy for anyone to estimate in an everyday kitchen with a ruler and a clock.

The shells might let the flavor through. Even if they did, at that point, it's too late. Due to temperature exposure, the egg white has changed state from liquidy to rubbery.

Once that egg white has changed to set form, a regular egg boiling session isn't going to change the flavor of a set egg white. The flavors can't penetrate into the set proteins.

Long term methods can be applied to get curry flavor into a hard boiled egg, like this Garlic-Curry Pickled Eggs. But understand there will be a strong vinegar taste as well.

I have tried multiple way of getting simple regular seasoning inside of boiled eggs. From heavily salted water to a seasoning used to boil seafood, the eggs never took on any flavors. It’s psychological that you think they take on a flavor without sitting in it for a greatly extended amount of time, as an earlier reply said!

not at all sure how someone could say that they have boiled in heavily salted water and/or seafood boil seasonings and say that they never took on any flavors! We routinely throw eggs in our seafood boils and sometimes boil only eggs in crab boil or other seasonings( Old Bay, etc) and the eggs ALWAYS pick up flavor. Can not believe that someone who claims to have tried this can say there is no flavor picked up by the eggs.