I understand you can change white balance to another value, but that is not my point.
If you take a picture of a gray card in direct sunlight with camera white balance set to incandescent and another picture in direct sunlight with camera white balance set to fluorescent you can't use the gray card image to correct white balance in the second image with Nikon Capture NX, but you can with ACR. The test I ran indicates this is true.
Sure you can, at least in the Adobe products. The Raw data doesn't care. Its Grayscale. All the camera records is what it thinks is the illuminant based on what you set and writes some EXIF data. But the Raw data itself isn't affected. You can use the EXIF or ignore it. Or render the WB any way you wish.
IF NX will not let you alter the WB based on the EXIF data, its a royal mess. But I can't comment on that product, I can't use it.