rdbates,
I haven't tried it, but I think organic grease is more soluble with temperature, and washes off, while greases from petroleum products don't solubilize as readily with hot water.
I would be careful putting items of this nature into a non-explosion proof environment. I could see the timer on the dishwasher going from wash to rinse, and in the process igniting the vaporized mixture of petroleum products (grease) and sending the dishwasher into the neighbors backyard.
Stuart