Anticipating that I already had the answer, which is that there is no built-in worksheet function that returns the background color of a cell, I decided to review this article, in case I was wrong. I was amused to notice a citation to the very same MVP article that I used in the course of my ongoing research into colors in Microsoft Excel.
While I agree that, in the purest sense, color is not data, it is meta-data, and it has uses as such. To that end, I shall attempt to develop a function that returns the color of a cell. If I succeed, I plan to put it into an add-in, so that I can use it in any workbook, where it will join a growing legion of other functions that I think Microsoft left out of the product.
Regardless, IMO, the ColorIndex property is virtually useless, since there is essentially no connection between color indexes and the colors that can be selected in the standard foreground and background color pickers. See Color Combinations: Working with Colors in Microsoft Office and the associated binary workbook, Color_Combinations Workbook.