OK so we all know that the baby son, Shaun, is going to survive. That's going to be the "grand reveal" at a later point in the games main quest. There will probably be a baby skeleton in the vault at the start of the game or something to try and make you believe your son died, and the major twist will later reveal that was not Shaun.
What makes it so obvious is that the focus on the couple having a baby in the first place, baby actually has a specific name and that he is generated as a mix of what the player makes the parents look like. Clearly points to the fact that Shaun will be an actual character at some point later in the game.
But would it not be interesting if Shaun basically turns out to be a chip off the old block? If you spend most the game being evil, Shaun will be a horrible leader of some crazy cult/group. If you do good deeds throughout the game, he will be the leader of a righteous faction. Your actions will alter the course of the story in a dynamic way. That would be cool.