I don't want to knock machine learning. There's a very huge set of very interesting problems that it does solve that were basically intractable till now and we haven't even scratched the surface of applications for. But the existing techniques have understandable restrictions to the scope of soluble problem.
I would also not be surprised if the best models included current ml strategies in some way, for example, in supervisor threads or initial processing of complicated input data into semantic-ish vector valued forms.
I think there's a chance it could in principle. Or at least, I think it could yield something close. If human intelligence is largely rooted in a neural network with billions of neurons and trillions of synapses, then it seems reasonable to think that, in principle, a sufficiently deep/wide ANN could show "intelligence".
But here's the rub. Doing that would be silly. We already know how to make a neural network with human like intelligence using billions of neurons and trillions of synapses... it just takes a man, a woman, and about 9 months. :-)
Also consider the power consumption of an ANN of that scale, given the current state of things.
So yeah, to achieve anything truly AGI like, which doesn't need it's own nuclear power plant, I suspect we're going to need other approaches in addition to today's ML/DL stuff.
I went to a talk from people who had built more scalable training algorithms for Restricted Boltzmann Mahcines (which Hinton was a pioneer in) a few months ago and asked them why they had chosen to use RBMs. Besides the waffly answers about how generative models were more interpretable than discriminative models, the real answer seems to have been that this was a research program that had started when RBMs were still in vogue, and their funding was tied to it, and once it ran out they were going to switch to investigating Generative Adversarial Networks like everyone else.