If you could answer a few questions for me so I can better assist you.
Were the eggs cracked or did he eat the shell and all?
How long ago did he eat these?
Dogs have very hardy systems and can handle a whole lot more than us. Dogs do not get e coli or salmonella poisoning easily, but it can happen in some rare instances.
Some people who feed an all natural raw diet put eggs in their dogs food daily and sometimes the shells. Some people add it to a dogs food to make his hair coat shiny. Yes, I would say six is alot but as long as he does not continue a diet like that then he should be fine. If the eggs were sitting out for awhile, as in overnight, then he might get diarrhea and possible vomiting.
If you do see some diarrhea which could be coming soon if his digestive tract becomes upset then start him off on some bland foods such as rice and boiled chicken until the diarrhea subsides and slowly start adding in his regular food.
Here is a website that you can go to if you have any vomiting or diarrhea issues that could follow.
I hope that I could ease your mind a bit. Let me know if you have any more questions.