In the eggs of most birds and reptiles, the chalazae are two spiral bands of tissue that suspend the yolk in the center of the white (the albumen). The function of the chalazae is to hold the yolk in place.

no and no it holds the egg together

Chalazae (white strings) are there to anchor the yolk in the centre of the egg shell.

You must mean that stringy white stuff beside the yolk of an egg. That's not an umbilical cord. What you see is called the chalazae. Chalazae are strong protein strands designed to hold the yolk of the egg centered in the albumen (egg white). The chalazae in a real fresh egg are quite noticeable. They shrink or disappear as the egg ages in the shell. There is no umbilical need for avians (birds) since they are ovipositors. Egg layers have no need for umbilical cords as development takes place in a separate closed environment from the mother.

The twisted strand in the egg white that anchors the yolk is called the chalazae. There is no health risk in eating this part of the egg.