I am not sure I understand your first sentence. The egg would have to come from a hen that has been treated with an antigen (the spike protein).Right, so if taking an uninfected egg with antibodies that the chicken already has in the egg to protect the egg, would that not help boost the immune system? Therefore possibly preventing covid or other colds/ flus? If the egg is protected from various bacteria/viruses because of its antibodies, logically speaking it would help the person eating those antibodies.
But more broadly no, the antibodies are very specific not generally protective.
So if you get infected with Covid then it is anti-Covid antibodies you need.
And there is one other wrinkle which is the antibodies would get destroyed in the stomach if eaten so they need to be injected into the blood stream (please do not try that at home - even the smallest contamination can be fatal).