I really don't think it's a big 'if'. As long as there is human level performance data, neural networks can be trained to match that level of performance. So it's a matter of time. It is indeed very, very hard, but also solvable.
However, the process your describing, of collecting human-level performance data, requires the ability to gather all of the data relevant to the act of driving in a manner consumable by the algorithm in question. This is the simulation problem, and it's very, very, very hard (it's why genetic algorithms have traditionally not gotten much further than toy examples, in spite of being a cool idea). Perhaps it is the case that it is very important to have an accurate model of the intentions of other agents (e.g., pedestrians) in order to take preventative action rather than pure reaction. Perhaps it is very important to have a model of what time of day it is, or the neighborhood you're driving in. The likelihood that it is going to rain some time in the next hour. Whether the stock market closed up or down that day.
It also assumes that neural networks (or the more traditional systems used elsewhere) are sufficiently complex to model these behaviors accurately. Which we do not yet have an answer to yet.
So, when I say, 'a big if', I mean for the foreseeable future, barring some massive technological/biological breakthrough. That could be a very long time.
