Yes in general this works. Works to the limit of battery capacity and two batteries may not last long. And assuming this is a 30 amp RV really needs 3600 watts to run everything normal, the 750 watts will limit what can be run.
Microwave, A/C, electric water heater must remain off. Fridge must be set to propane only or may draw 350 watts near continuous and drain the battery. Most coffee makers etc are 1000+ watts.
Run a small tv, charge phones and a laptop is all good. What else do you expect to run?
There are some inverters that cannot be connected to the RV system and the RV battery as they don't like the negative battery and inverter sharing the same ground. Need to isolate the battery so that it connects only to the inverter.
