In a few words: Probably not. But let me explain further.
Eggs are high in Saturated Fat and have very little else besides Vitamin D and B12 (which it only has a little of) that could be of any use. However, I am not going to mention Cholesterol when talking about eggs, as the latest change to the Dietary Guidelines mentions this:
“Cholesterol. Previously, the Dietary Guidelines for Americans recommended that cholesterol intake be limited to no more than 300 mg/day. The 2015 DGAC will not bring forward this recommendation because available evidence shows no appreciable relationship between consumption of dietary cholesterol and serum cholesterol, consistent with the conclusions of the AHA/ACC report.
However, eggs are high in saturated fat, which the change constantly mentions should be avoided if at all possible, but does note that it is almost impossible in this day and age to eliminate ALL saturated fat from your diet without suffering the possibility of nutrient deficiencies.
The issue is, the argument on Saturated Fat alone does not really help the Vegan cause, mainly because a typical serving of most nuts or seeds contain the same, if not MORE, Saturated Fat per serving as eggs do. This is not to say that eggs are in any way healthy, but that they are not the worst food in existence in terms of Saturated Fat.
Eggs do have a low enough amount of Saturated Fat so that you can include them in a healthy diet as long as you keep the eggs to a minimal and not add too much more saturated fat into your diet. However, there is more to think of in terms of egg consumption, for instance:
142,000 people get salmonella food poisoning from eggs on an annual basis. Although this is not the main cause of Salmonella, as 80% comes from poultry, meat, eggs, and even fish. The CDC notes that only 18% of Salmonella Outbreaks come from Eggs, and a very similar amount of Salmonella poisoning also comes from fruits, vegetables, Legumes, Leafy Greens, and nuts. Although avoiding animal products and eggs would definitely lower your risk of foodbourne illness, calling out eggs in specific for Salmonella seems a bit disingenuous.
Another issue that I have seen with eggs is that there was a study done in 2012 which brought the results that the consumption of egg yolks were as bad for you as years of smoking. However, further insight into this study finds that it was incredibly flawed, and only mentions a correlation, as well as the study completely ignoring input of many other dietary and health factors prior to publication. In fact, studies have shown that egg consumption of even one egg a day does not have any adverse effects in terms of Coronary heart Disease.
Minor consumption of eggs per day, such as an egg a day, is not seen to be unhealthy in most individuals. However, like with everything, moderation is key. Keep egg consumption at a minimum, but you don’t have to fully exclude it from your diet to be healthy. There are, however, moral reasons to not eat eggs, including the harm done to chickens as a result of factory farming, but healthwise there is no reason to exclude eggs from your diet.