You know what, I in fact had been pondering whether this would be a cool feature for a project I had a while back. I’d say it kind of depends on the nature of the website and, more importantly, who your users/customers are.
Only you know what the project is about.
You should therefore have an idea of who a potential user could be (create a persona).
Based on this information, do you believe that easter eggs could be of interest to that user and/or of added-value to your website?
Take video games for example. All games are games, and all users are players, but not all players are the same. How do you define which game fits the egg criteria, and why is it relevant to said game and type of player?
Facebook could have been the kind of platform hiding away secrets, such as easter eggs. After all they did mess around quite a bit with the poke button. Did the poke button bring any added-value to Facebook? And thus, would an easter egg?
What I’m trying to say is that, ultimately, this is up to you. Only you know the project, and your potential users/customers. Only, when you’ll make the decision, be sure that it will impact your website the right way.