I've wondered that myself. What happens if I mix my white and blue or white and splash, mottled? I guess I'll have to wait and see what happens when i try it.
White is not a color. It's just a gene that prevents whatever color the bird has from showing up visually. A white bird could be genetically a solid black.. crele.. mottled or whatever, just you cannot see it at all.
What happens also depends on another reason: there are two white genes, Dominant white and Recessive white.
Dominant white x splash= very likely a white bird with few minor flecks of blue. This is because only one copy of Dominant white doesn't always turn the bird completely white.. two copies does a much better job.
Splash x Recessive white, either all blues or all blues with color leaking on the necks and saddles, if the white was a brown not black base- then it would be the same as crossing a splash with a partridge.