I think no.
He still has yet to deal with some of his own issues (the death of Obito, Rin, and sensei) and trying to balance his duties as an ANBU. Making him babysit through an orphan when he himself is developmentally, emotionally and psychologically not ready to deal with it will not do well to his psyche, as well as Naruto's needs.
Granted that it would have been nice to see him show a semblance of care for Naruto while he was growing up, but I think it was best to leave him to deal with his issues rather than be a full-time caretaker for Naruto.