Yes but not very well as it is not a complimentary circuit and cannot provide as much current towards the +ve rail as the transistor relaxes, as towards the -ve rail when the transistor is working. I would think it may be reasonable though.
There's so much wrong with this circuit as a headphone amp.
With so many circuits available, why build this? It's low impedance input and not very linear. I don't think it could even drive an iteration of itsself. You'd be way better off paralleling a couple of 5532s.
This is the kind of circuit you'd build in a beginning electronics class. It really doesn't have any practical use at all.