I have used my Kill-A-Watt to measure converter 120v draw when going full out on a low battery, but not when running typical small RV loads.
My instinct (for what that is worth!) is that you might have a situation somewhat like a water heater, where it is easier to keep it hot than it is to get it hot from cold. Or VV with the fridge.
The battery will cycle without the converter, and solar picking it up when it can. If you need to use the converter to bring up a low battery when solar can't, then I think you will use more 120v draw than if you had just left it on Float and run whatever 12v things need it at times.
Cycling the battery also uses up more money, buying batteries sooner, but you can lose your battery from neglect while on converter too.
The real money might be from using an inverter to run all 120v things except air conditioning, if you have enough solar coming in to keep the battery bank up. But that also cycles the batteries and you need more of a battery bank, which all costs money.
Propane is another alternative to 120v for some things. Depends on the math for that if there is anything to be saved there.
Also there is the question of how many days per year is this all about. A car that gets 30 mpg is not an advantage compared with one that gets 10 mpg, if you don't drive it many miles a year.
It's like LED lights in your RV. Only worth it if you have the lights on a lot during a year, and 12v power is in short supply.
People forget that amp-hour means over time, not just the amps.