I, too, will be doing breeding experiments by this time next year. I may very well use dyeing in the shell to identify chicks from different breedings. This could help me learn right away which pairings produce the healthiest, most vigorous chicks, and later learn which ones develop the desired characteristics I'm breeding for.
This is a valuable tool used by many breeders. I like it a lot better than "toe punching" which involves using a device sort of like a paper punch to cut off the webbing between the toes of baby chicks. The thought of that makes me ill. Chicks are identified by the pattern of cut-out webbing. I'd rather dye them, and leg band later, as they start to feather out.
I don't see how this is disrespectful to the animals. Breeding at random without regard to results seems disrespectful, to me.
The fact that the dyed chicks are cute and colorful is just a side benefit. Does it make us disrespectful to enjoy the colors produced while we're monitoring the health and genetics of our chicks?
I might try the food coloring in the feed, on one hen, just to see what happens.  How much food coloring does it take in the feed? It would seem to me that it would take a lot, to saturate the hens system, and since the ovules are already formed on the ovaries when hen begins to lay, if the dye truly saturated her ova, then all her eggs from then on would produce dyed chicks. Unless the color is somehow flushed back out of the egg yolks. Seems like it would take more than a couple days.
I've had birds eating poke berries  and pooping purple for days, and saw no color change in the eggs I was collecting. So I'm skeptical. But I could be wrong. 
I searched and searched, and found no other reference to dyeing chicks in this manner. I did find lots of references to dyeing chicks by injecting dye in the eggs, and a few on dipping new-hatched chicks in dye, (which sounds dreadful to me, they could aspirate the liquid into their lungs and die, which won't happen with shell-dyeing) and spraying or wiping color onto the new-hatched chicks, which, if you just want pretty colors, is ok I guess, (though more traumatic for the chick than just hatching out already that color) but useless for I.D. purposes, since, as I said before, you can't tell which shell the chick came out of, unless you're watching constantly, opening the 'bator, and taking out chicks as soon as they hatch and coloring them, then putting them back in to dry and fluff. Doing anything like that can seriously hurt the rest of the eggs, not to mention chilling each new hatchling.
Raynie, thank you for posting about dyeing the chicks, I've thought about trying this before, and perhaps now, I will.
Ellie, I appreciate your thoughts, but this really isn't the same as dyeing chicks to sell as a novelty. (which I would never do, or condone) And, when introducing the dyed chicks to the rest of the flock, that's usually not done until they feather out, because prior to that, they have to be kept warm in a brooder. Once the feathers come in, almost all the dye is gone. If you have several colors of birds anyway, the potential for attack because of odd coloring in very small. The risk of attack due to age and size difference is much higher.
I'm not trying to argue, just explain how dyeing is a useful, valid tool in breeding. Though it can still be fun to see the results, just as I have fun seeing the results of breeding chickens in the first place.