Many do not like the tankless water heaters in a RV. THis is because the input water can be really cold when camping in the northern states, say 40F. It can only warm the 40F water by about 50F at a decent flow rate, so cutting back the flow rate you can get warmer water, but less than a gallon per minute. You live in the south, where input water will be at least 60F, so that should not be a problem for you.
Also if you are dry camping, then the water flow can be variable, creating problems. If there is to low of flow, it will overheat and shut the burner off, giving a instant cold shower for a few seconds until the burner comes back on and warms up the water again.
Hopefully they have worked out the problems with the instant water heaters over the years. Did the dealership have any other units with tankless water heaters - so you could listen to one?
If you have the brand specs, it would be easy to look up how much gas it can use in one hour. Basically there is 95,000 Btu's in a gallon of propane. A normal water heater is 8,800 Btu's for the 6 gallon model and 10,000 Btu's for the 10 gallon tanks. I would expect the tankless water heater to have a 37,000 - 45,000 Btu input rate.
I have a tankless L5 water heater that was used to pre-heat the water going into my fresh water tank, when filling the tank (so it would be above 70F and I could enjoy a longer shower with my 6 gallon tank heater). It has a 37,000 Btu burner, and is rated to heat 5 liters per minute by about 45F. So 50 input (in the winter where I lived at the time) would have 95F output at 5 liters per minute, or about 105F if I slowed the fill process a little bit.
If you run into problems, send me a Private message, and we might discuss it at length.
You might find that running a bit of hot water into the fresh water tank solves any problems while dry camping to keep the water supply warm enough. If your outside shower can reach the fresh water filler, this will work great. In my class C motorhome, I installed a fitting on the sink to flush the toilet with a garden hose. With a 25' long garden hose (drinking water quality) I could have refilled the fresh water tank with hot water if I had wanted to.
If you are ever in a campground, and the water is to cold to get a good shower, try running the fresh water pump, and it should provide warmer water than the campground water input.
No matter the gas input, the water heater will not burn more than the older conventional type, as it runs less minutes per shower, or less minutes each time you do dishes. Expect total gas usage to be about the same, with the exception that if you start to take showers twice as long, because the water does not turn cold in 10 minutes, yes you could use more gas on a long shower.
Either way, a gallon of propane is only about $2-$3, and will run the heater for 2 full hours or more. So each weekend trip might include 1 hour of water heater run time, really in-significant cost of the total trip.
Good luck,
Fred.