Selected Answer
No. That would not be possible. Here is the reason.
A cell can have only one color, just as it can have only one value. However, just as it is possible to display a cell's value in different formats so it is also possible to display a cell in a color which is not its own. This is the principle on which conditional formatting works: a cell has no color but it is displayed red.
In this scenario, if a formula would look at the cell and determine its color it would find that the cell has no color even though it is clearly and obviously red. The same, by the way, would hold true for VBA code examining the cell.
Now, imagine a formula which changes the cell color. Would it change the real cell color or would it just display the cell in another color? Excel's principle is that no formula can change any cell's own properties. To do so is the prerogative of the user, exclusively, or of VBA doing the user's bidding.
Therefore the answer to your question is that if you wish to change the apparent color of a cell use conditional formatting. On the other hand, if you want to change a cell's real color use VBA.