When talking about vitamin and mineral content:
An egg can create an entire baby bird. Every cell in that baby bird needs the whole gamet of B group vitamins, as they are essential for the processing of sugars and fats to form energy and amino acids. For functioning eyes to actually develop, vitamin A is needed for retinol, the pigment that lets you see. Vitamin C isn't required in the diet of snakes. Vitamin D is required for the full development of the musculoskeletal system. Vitamin K is responsible for the creation of clotting factors, and without it things haemorrhage and die.
For the heart to beat, the brain to work, muscles to contract, and the kidney to function there has to be adequate amounts of potassium, calcium and sodium left over. Indeed, by blocking K/Na-atpase (a channel for the shunting of sodium and potassium ions) results in pretty quick death.
The only one I can't comment too much about is vitamin K, but I suspect that it's not required as much in reptiles. The main function of it, at least in humans, is an antioxident; however, this shouldn't be as much of a problem for reptiles as it is for warm-blooded animals.
Warm blood = faster metabolism = more reactive oxygen species = greater demand for antioxidents.
Also of note, although this I can't say for certain occurs in reptiles, but would in mice, half of the vitamin K requirement is synthesised through gut flora, and not dietary.
And, yeah, the shells are calcium carbonate, which is digestible as acid removes the carbonate and so you are left with, essentially, calcium chloride.
All in all, yes, eggs are nutritious. One of the problems I could foresee is that a lot of the calorie content is made up from fat (~<60%), and I'm not sure how well snakes deal with high fat contents. But, hey, there are specialist egg-eating snakes. Can anyone clarify more on this for me?