Wish I did - I had excess eggs yesterday (sales have almost stopped, now that the local teachers are our of school and without paychecks) so I threw 30 raw eggs to my flock of 50+ on the pasture, but I will only do that once or twice a week while egg sales are slow and production is climbing (would be worse if some weren't in molt).
Somehow, I doubt its been much studied - I've certainly seen nothing.
Here's what we do know -
1) Eggs are a complete protein, they contain all the essential amino acids, so that's good.
2) By weight, Its about 11% protein (that's low), 8% fat (that's high), and insignificant amount of fiber, and a lot of water.
3) Salt sits at 0.44%, right in range of the typical commercial feed. Its also low in phosphorus (0.15%, about 1/4th what you see in many feeds), Selenium around .20 ppm (2/3rd what I see on a bag of Nutrena All Flock) Using the same comparison (and if my math is right, its got half as much Vitamin A, half as much D3, and an insignificant amount of Vitamin E.
??? But perhaps more is contained in the shell? I've no idea how much calcium, phosphorus, etc is in the shell of a medium large egg ???
4) and it looks like egg shells are as much as 40% calcium - if you find your meaties or your favorite Roo eating the shell to get the yolky/albumin goodness, you want to stop that. They are apparently good sources of magnesium and phosphorus. Sadly, a high source of sodium.
So, based on what I've just discovered crawling the web (THANK YOU, learned something new before lunch!!!) I'm going to stick with my normal recommend for treats - not to exceed 10% of diet by weight. Rough math time -
There's about 455 grams per pound, and a "typical" chicken eat 1/4 lb per day, or about 115 grams daily. 10% of that is about 12 grams, and a large egg is about 58 grams w/o shell, about 64 grams with.
So, don't exceed one egg per five birds - and that's about 3.8% calcium by weight if you include the shell.
Helpful?