Sankey is about proportional-width bands, but the chart in your sketch just uses a set of fixed-width paths, using the cubic bezier curves that Sankey typically employs. And what you want the ends of those paths connected to is not a set of independent nodes, but two ranges, with positioning determined by your data values.
So the Google Charts Sankey diagram is not going to help much. I haven't seen anything quite like it as a standard chart type, so you might have to roll-your-own with something like raw d3.