Explicitly not counting any egg(s) that are part of the bread-baking process.

Eggy? Interesting question. Not necessarily, and not in its own right. But there are versions of this that would include egg as an ingredient, I think.
Shergarburger? No.

[Chalky] You have taken the very wind from my sails!

Unique? No. (A unique sandwich??)

Edible? I certainly hope so. It's a sandwich!
Sauerkrauty? It's possible (I can find examples online), but it is certainly not an essential or even a standard ingredient.
Fishy? It sometimes contains fish, yes, but need not. For free, I will tell you that it is quite common for it to contain other seafood, however.
Croque monsieur? Non, madame.
Clarification on the egg: my reply was meant to imply that it would be very unusual to see egg listed explicitly as an ingredient, and I stand by that. But googling reveals that it is not unheard of.