The "neural net" system of "AI" we use today is a grand way of self-organizing a statistical filter. Will this create intelligence on its own? There's no reason to think so, unless one is incapable of critical thinking. See the other comments here for some examples of an inability to think.
What the current batch of "AI" can do is recreate something that statistically and realistically looks like intelligence, at least some of the time. The deficiencies of this technology, and the downsides of its use and overuse, become more obvious every single day. We just have this great set of math, and machines that can do the math quickly, that pull patterns from large amounts of data. Feed a ton of human data, then get a pattern of human behavior. It does not make actual human behavior or thought, of course.
That said, to create something that is effectively intelligent, effectively capable of everything a human can do, I do believe that neural nets can play a role, especially for things like image recognition. What to do with that recognition is a whole other thing, though, and that is where something else needs to be invented. Also, there is a lot of room for leaps forward in the current neural net state of the art. I think, though, most efforts are focused on processor efficiency and experts, instead of trying to transform the science of the software.