If Faye went straight to the Diary Room after Aaron tried to explain why he nominated the way he did, then I'd say the relationship could easily be over.
Just as she was walking off, I think Aaron was about to tell her he'd put her first in real life (presumably after his son) but that this was a game show. However, he hesitated and didn't chase after her because he was annoyed about her reaction and the fact that she didn't understand him.
Unfortunately, I think Faye may have said things in the DR, that will make it difficult for them to get things back to how they were before. And even if she didn't, I think Aaron will suspect that she has, so it's going to be much harder for him to say the thing I think he was trying to say. And I'm not sure she'd believe him even if he did.
The only chance for the relationship is if the person in the diary room asks Faye what she thinks Aaron was about to say as she stormed off, and she goes back and asks him. Because I'm not sure Faye will twig herself.