Moore's Law is about transistor density, not computing power, so no it won't.
We could probably already build a computer more powerful than the human brain, it would just be huge (millions of cores or something). But that wouldn't help, because the real issue is that the Von Neumann architecture fundamentally prevents scaling the kinds of computations we want to do for neural networks. We need something more neuromorphic, although probably still discrete. (I'm guessing basically just a giant DSP integrated into memory on the same core.)
We could probably already build a computer more powerful than the human brain, it would just be huge (millions of cores or something). But that wouldn't help, because the real issue is that the Von Neumann architecture fundamentally prevents scaling the kinds of computations we want to do for neural networks. We need something more neuromorphic, although probably still discrete. (I'm guessing basically just a giant DSP integrated into memory on the same core.)