I don't think 2,000 years is enough, but am not an expert. The main thing that grains and bread did was make it a lot easier for more people to get through lean times without starving. It also allowed people to specialize: not everyone needed to be a hunter/gatherer.
20,000 years maybe yes. But we have not been agricultural for that long. And that's why grain-based food still is not something we're well adapted to.