Our Muffy and the (4) other cats preceding her have always used "Tidy Cat" brand litter. I once did what you suggested Henry, and used it as an anti-skid spread on icy sidewalks. As the weather warmed up and the ice melted, the litter turned to mushy mud and tracked all over, including into the house. That is the only reason I felt it would flush out with plenty of water.
Maybe my mistake was using new litter and not letting the cat condition it first?
Regards,
Dodgeman