If I remember rightly oil is not as efficient at heating as water (water is quite exceptional at transferring heat), so if you did that I suspect you'd have to leave everything in there for a lot longer to get it upto temperature. So any money saved heating will be lost in the longer cooking times. Not to mention that oil is far more expensive to begin with.
There is an experiment you can do to show how good water is at transferring heat, I forget exactly what temp is best to use but basically you bring a pot of oil to 75c and a pot of water to 75c. You can leave your finger in the oil for a good while before it starts to burn but the water will start to burn you almost immediately.
mso-fareast-font-family:"Times New Roman""> During initial heat up, when theunit is simply ramping up to temperature, the heater is on at full power. Theunit will consume about 1.006 kW/h during this stage, which should takeapproximately 60 minutes using your example temperature (56c). This stepcan be greatly shortened by starting with hot tap water. "Times New Roman"">
mso-fareast-font-family:"Times New Roman""> Once desired temperature isachieved, the unit goes into a much lower power state to control temperature,using about 15-20% of the maximum power. This equates to a maximum of about0.21 kW/h of power consumption when at the maximum cookingtemperature (85°C) Power consumption decreases at lower cooking temperatures; Iwould estimate 10-15% at 56°C or 0.16 kW/h at 56°C. Other variablessuch as ambient temperature, the use of a lid, insulation, etc will causeadditional variance in these values."font-family:"Times New Roman","serif";mso-fareast-font-family:"Times New Roman"">