How about:
- Produce an RGB raster
- Exporting to vector
- Loop through each polygon's centroid and interrogate the rgb in the raster
- Put the RGB value in the polygons attribute table (maybe you could ninja / modify a bit of code from the link below)
- Symbolise a layer file for your range of RGB values, and apply that to your newly attributed vector polygons
[SAVING RGB VALUES INTO A POLYGON ATT][1] [1]: https://gis.stackexchange.com/questions/124401/saving-a-arcmap-layers-rgb-values-into-the-attribute-tableSAVING RGB VALUES INTO A POLYGON ATT