Random header image shouldn't load when custom dashboard background is set

I have set a custom dashboard background image. When I don’t set a header image, the background fills the screen on the dashboard, including the header (so there is no visible header border), which looks great.
However, if I enable random header images, these still load on the dashboard, creating a very unattractive effect (the header has its own custom image and the dashboard background only starts under it).
Should the header image be made not to show at all in the dashboard instead?