I see no reason not to try this. They definitely do eat eggs and I've heard of people doing it with no problem in captivity. I would of course not use it as a staple, and I suggest that you mentally prepare yourself for the messiest poop you've ever seen.
As far as complete nutrition and variety they do just fine on rodents and only rodents, as well as just one prey item for their whole life, and although I see no reason to switch things up much but that's just my opinion. Nothing wrong with a bit of variety in most cases, but it's sometimes a "new school" thought that's presented to fix something that isn't really broken, but I'm sure that's not the case here nor is it on this forum.