The Gemini catamaran has a propane refrigerator, so that load is not factored in. Might be too much for a Honda 2000 with both AC and 12V fridge going at once.
Running the circulator and fan off the inverter allows the Honda to absorb the compressor startup load without popping the breaker. Yes the inverter will reduce the efficiency somewhat, but it will be way more efficient than running two Hondas as some owners have done or going to a much larger and heavier
diesel genset ($10,000+?)
Others use the Yamaha 3500 but it is larger and bulkier to stow.