Vegetarians can eat eggs. They aren't killing an animal in a tortuous way by doing so.
Eggs are fruit. In Australia we call them cackleberries.
Seriously? Eggs are potentially chickens in embryo. That makes them animals. Well, flying animals. Or in the case of chickens, fluttering animals. Sort of.
If by "veg" you mean, "Can a vegetarian eat them," then, Yes. Many do. If you mean "Vegan" then most certainly not. No true Vegan would traumatise an embryonic chicken, potential or otherwise.
What is "veg"?
If you mean "vegan" ... No, they can't eat eggs.
If you mean "vegetarian" ... MAYBE. Some vegetarians view eggs as animal, while others don't. Of course, some vegetarians think it's okay to eat fish.
If you mean "vegetable" ... Obviously not.
"Vegans" eat no animal products, like cows milk cheese, ect. Vegetarians do/can, just not meat.
It depends. They are a good source of protein, and if the vegetarian is averse to animal by products, it should be acceptable. If the person were a vegan, then eggs and dairy are off the menu.