I feel like if that happened with a human it would be a pretty minor thing to go up in there and smash the egg so you just shit out the shell and stuff. I don’t really see a reason it would have to be fatal, or even really all that big of a deal, if that’s just what human reproduction looks like.
Now if we were using the cloaca in the same way we presently use the vagina, as a birth canal for developed offspring, that would be a different story, but ultimately not all that different from now.