So atm if you pick up one of the water machines (the ones that have the two knobs and the huge water drum on top) and move it, it won't dispense water if the water is off. I suggest that water machines work like water storage.
If you find one, you can remove the water tank (just like you can remove the propane tank from the grill) and then move the machine. If the tank originally had been holding water the water will spill out leaving you with an empty, but movable container. Full containers can be added after moving to provide a convenient water supply in your base that is refillable.