It will be, by a factor equal to the inverter efficiency as the elements are all 100% efficient. So if your inverter turns in say 87% efficiency then the 12V element will add that missing 13%. In reality, the difference between operating the element at 230V or 12V is likely to be overshadowed by other considerations, such as the quality of heat insulation on the cylinder and suitability of the exact volume that is being heated. If you had a really well insulated, ideally sized 230V heater, I would favour running that on the inverter versus using the 12V direct in a less-well engineered tank setup.
However, 800W is starting to push the limits for 220Ah storage albeit more convenient for a faster heat-up time. Allowing 90% inverter efficiency that would correspond to a discharge rate of over 70A at 12V or C/3 (entire nameplate capacity discharged over 3 hours) and whilst that is bearable, the cyclic efficiency and durability of a leisure battery will be tested. OK for a full traction lead-acid or Li-Ion but on the limit for leisure or semi-traction. You will probably lose 5-10% of capacity by working at that element power. If you have a 230V heater that you like but want to limit the power so as not to stress the batteries by a high discharge rate, it is relatively simple to use a bucking transformer to reduce the power without impacting inverter efficiency. (Note that reducing power with phase-angle control can dent the inverter efficiency quite badly).
On our boat, I have used a transformer to allow different heat inputs to the water when running from a shoreline with limited capacity. E.g. if I've only got 10 amps but want to run the microwave and a cabin heater, I can throttle back the element to 1000 or 500W to save some amps. As we have many other heat sources, I've never been tempted to run that on battery although with 660Ah domestic storage it would be possible in an emergency.
We're relatively old-fashioned in having LPG wet central heating instead of diesel. On the plus side, it's very effective, quiet and reliable. Just press the button and everything's toasty in a few minutes and you can start showering 15 minutes later (and never stop, if you don't want to). But it's getting very spendy with the current price of Calor gas and would be difficult to justify the cost if it were the sole source of heat. Thankfully, we can heat the cabin with solid-fuel and the water is always heated by the engine when it's running, with enough stored for a few showers. So in the summer, the boiler is only needed occasionally and it would take a while to recoup the cost of switching to diesel, plus I doubt any diesel-fired heater would run faultlessly for 30 years as our LPG Alde has done.
Obviously in a boat we have more cabin side space for wet rads and they are not necessarily practical for a van. This is a pity because diesel-fired wet-central heating is effective and economical and the most versatile if you can also use it to heat the water in a regular calorifier. If you get one with a good coil that can absorb a large percentage of the heater output, very fast reheat is possible. Whether fan convectors and a wet system makes sense, I am not sure, and clearly other people have the same thought hence the existence of the Truma Therme.
Take care with respect to legionella; hot water should ideally be heated to 65°C for safety.
