This is a really interesting question. I think the answer is a combination of both—I think it's important to the arc of the story that John does literally faint, particularly given the background of the narrator's health issues. John, as a doctor, and as a dominant male, has set himself up as guardian of his wife's health: he has disregarded her words because of a feeling that she is too feminine and weak to understand herself, and has decided what is best for her is to be cooped up here in this house. Fainting had (and indeed has) strong associations with femininity: fainting is an indication that a person is not physically strong enough to cope with what is going on. For John to faint here, then, represents a victory for the narrator. Instead of she being the weak one, it is he who is physically overcome by the situation—he has been proven wrong. He is domineering and he thinks himself rational; but he can't cope with what he is seeing. It literally floors him to realize what has happened to his wife, and that it is the opposite of what he thought would happen and intended to happen.
Then there's the point at which he faints, and the subsequent comment that she has to "creep over him every time," suggesting an ongoing pattern. This part, I think, is symbolic—he faints in response to her victorious assertion of dominance over him: she has "got out at last," "in spite of" him, and now he can't "put [her] back." So, it's important to end the story here, because it represents a symbolic victory for the narrator: she has knocked down, as it were, the domineering figure of her husband and now will continue to trample over him, keeping him down, as it were. It's as if by going mad, she's actually able to be herself for the first time ever. She has defeated him by proving that his medical science was the opposite of what she needed, and now because she is beyond rationality, he is unable to reach out to her any more or make any attempt to "put [her] back" into his prescribed boxes.