Statistical uncertainty grows like sqrt(N), and percent statistical uncertainty shrinks like sqrt(N) / N. So 2000 samples has a percent statistical uncertainty

Statistical uncertainty grows like sqrt(N), and percent statistical uncertainty shrinks like sqrt(N) / N. So 2000 samples has a percent statistical uncertainty of about 2% - this is likely on par with or smaller than the systematic uncertainty (errors which don't depend on the size of the data). This means 2000 samples is probably fine for what they are trying to do, especially because the dataset is balanced with each class having 1000 samples. However the more data you have the better your model will do.