Yes but at the end she's so distant and almost "broken" and Joel's in such happy denial. Complete role reversal, and it kills me. I felt that if he tried to sing or teach her guitar she'd still be unresponsive. Joel still had his defenses up when she asked him to sing and he was still trying to separate himself from her, but after Winter they both completely change. He reclaims his role as a father and she is thrown into survivor-mode. There are little glimpses of her child-like innocence coming through, but I feel that at the end she still has an inkling that he lied to her. And I feel that we play as Ellie at the end to feel that disconnect. I feel that, if he did sing, that innocence and wonder she once had is still gone, and it would show even more.
I've been thinking way too much into the whole story/character development, haha XD I know they're making a side story DLC but they didn't mention which characters will be in it. It is open for a lot but I hope they take their time with it... The writing in this one was so great, there's no reason to rush another. I just have this horrible mental image of Joel and Ellie sitting round, him playing the guitar and her with a vacant stare. He'd play and sing for her and try to get her to learn but she'd just sit and play with the dirt or something and stare off into space. I think her expression at the ends shows that she knows he lied, but has already put so much trust into him (and he's her only father figure) so she just accepts it. I think it would break Joel's heart to see that innocence leave her, and I'm not sure how he would cope with it.
Leaving another daughter figure left to die he couldn't but now it's going to suck let's hope they don't do like The Walking Dead game where the DLC isn't about someone new and has nothing to do the story