In the story, the author says that she asks him this
just as if she had heard nothing of what had been said and almost as if waking up from a dream
To me, this means that you can definitely argue that she has not really heard all of what he has said. She must have heard some of it to know that he had a son, but maybe once she heard he was dead she sort of got lost in her thoughts.
In terms of the story, though, it makes sense for her to ask this. Because what she is really doing is confronting him about what he is saying. She is really implying that what he's saying can't be true if his son is really dead. He can't have those grand feelings if his son is dead.
She's right -- once he thinks about it, he dissolves into tears.
So to me, I don't know if it's believable for her to say it if this were real life. But for the story, it makes sense.