Hi,
Before I was full time I used to use my solar and battery bank to run the water heater, particularly when the battery bank was full for the day.
Jim, the ten gallon water heater on mine is 1200 watts and takes 90 minutes to reach full temperature. After that it cycles about every four hours and draws power for 15 minutes. My guess is that a 600 watt heater would take about 180 minutes to get to the first cycle.
If I know I will have shore power after a day's travel, I run my absorption fridge from the battery bank/alternator/solar/inverter. The fridge uses about 5 kwh per day.
For fun, in the past, I have heated the water using a five minutes on ten minutes off duty cycle, so as not to over stress the alternator.
If there is room on the roof for 1500 watts of solar and a hybrid inverter is used, it is theoretically possible to run the air conditioner. The cost works out to about double that of a Yamaha 3000 sIEB inverter generator.
I have run my roof air successfully from the inverter without the engine running on my class C. Because I have manual control of the alternator to house bank charging circuits, I am able to keep the duty cycle down to a safe level. I do use the fan only setting on the ducted roof air to help distribute cool air from the dash air throughout the RV.
I discovered last summer (before the hybrid inverter) that the roof air would cycle off when I ran it from the generator, when using the dash air.