I know that camera hardware does not return hdr values. So something in the actual conversion from/in the sensor (idk how cmos sensors work) would have to be affected by the white balance for changing it in the camera software to do lose a significant amount more information than changing it after the picture was taken. Unless the conversion from a raw image also is a factor, but raw images aren't hdr either so I don't really see how that could cause much significant difference.

If the white balance only dims colors and doesn't brighten them then it couldn't possibly clip anything and would have the same effect as lowering the exposure originally (with the new white balance) to avoid a clipped highlight.

I'm not a photography guy (just a computer graphics guy) so idk what the software usually does (I suspect it would avoid clipping? You could also brighten something with a gamma curve for example to prevent clipping...) but I can't find anything online about sensors having hardware support for white balance adjustment.