You can add fried egg later on top of the pizza. When you add the uncooked egg before baking, baking time will increase because the egg will not be done completely, especially if you like your egg well DONE.
I like my egg soft, but if you add fried egg later it is equally delicious and less time to cook pizza in the oven. Also, I tried this in the microwave... It was not the same, however, it was softer and still delicious. I made it like a quesadilla. You can add canned TUNA fish, or sauteed seasoned ground beef/or Italian sausages.