I don't know about your rig specifically. I know that I just drilled a hole through the floor way back behind our counter, then ran the standard power cord to the outlet in one of our bays outside. Then I caulked (with wire mesh to prevent mice) the hole that the cord runs through.
The water line has to be tapped into. We have PEX and used a sharkbite T to tap into our hot water line.
I think we cut into the PVC back there which was connected to the gray tank from both the bathroom sink and the kitchen sink. Put a T in that PVC, and turned it upwards, so that we could insert the U-shaped drain hose of the Vesta DW.
As far as plugging in the DW and running it, yes, it runs once plugged in. Just need to get the water situation sorted.
I believe the Fisher Paykel one is <1" taller than the Vesta and actually have it sitting in a friends garage in Tucson, ready to install when we get down there for the winter.