Hi Karl,
You should indeed run the energy balance calculations we discussed, to estimate the worst-case current drawn from the vehicle battery/alternator.
Someone in these forums has probably measured the AC power flowing into a AC200 charging brick. That (x2) tells you the inverter output power. The inverter manufactuer should tell you the (best-case) efficiency; reduce that by a bit for margin. Then DC power flowing into the inverter equals AC power flowing out divided by efficiency.
The second step is to estimate the worst-case (lowest) voltage at the vehicle battery terminals, while the engine alternator is running. I am not qualified to suggest a value. I think that when the vehicle battery is nearly full the alternator voltage is ~~14V. When the vehicle battery is hard-charging the voltage at the terminals is lower—perhaps 12V or less. (Others can give you more specific numbers.)
The third step is to estimate the voltage drop from the vehicle battery terminal to the DC input to the inverter. That can be made very small if you use large cable and have short runs.
Once you know the worst-case (lowest) DC voltage at the inverter input terminals, then you can calculate the worst-case (largest) DC current flowing into the inverter for the inverter input power calculated earlier.
Finally, we get to the hard part. Let’s say that you calculate the worst-case DC input current drawn by the inverter is 120 amps. The vehicle alternator will do its best to supply those 120 amps AND supply the worst-case loads of the vehicle’s electrical equipment.
The hard part is guessing whether the alternator in your vehicle will survive that situation. I use the work “guessing” very deliberately. I think you’ll find that there is no document that states the worst-case power drawn by the vehicle. And there is no document that states the maximum continuous current the alternator can produce under worst-case thermal conditions (slow driving on hot summer day). Without those specifications, adding electrical accessories to a vehicle is always a calculated risk to the alternator.