The hotplate through the inverter is a pretty big draw, but 3 100 Ah AGMs will certainly power it. The only question will be for how long, and how often, and what other things will have brough the batteries to a lesser state of charge.
Say the hotlate is 1200 watts.
1200 watts at 12 volts is 100 amps. A starter motor to start the engine is about 140 amps.
But the inverter is only 85% efficient or so, so bump that up to 1300 watts to run that hotplate off the inverter.
One thing to keep in mind is a 100Ah battery, earned that capacity rating powering a 5 amp load for 20 hours before the battery voltage reached 10.5v. 100Ah however does not mean the battery can power a 20 amp load for 5 hours.
The Peukert effect says the bigger the loadon the battery, the less overall capacity the battery will have to deliver.
So it is not just basic simple math when huge loads are involved, like a winch or big inverter powering a hot plate or coffee maker.
Simply powering a laptop is about 30 watts, but powering the laptop and recharging its depleted battery willbe closer to 80 watts.
3 100Ah AGM batteries is a lot of power though. you should be able to do most of what you want, on the first few outings. if you do not truly fully charge those batteries, but leave them at 85% for 2 months before the next outing, they will have lost a significant portion of their capacity and not be able to deliver as much. Without careful monitoring of voltage under load this might still go unnoticed. Most people will not notice when a large bank of batteries has degraded until the low voltage alarm on theinverter starts screaming well before it is expected. At that point they learn their batteries are capacity compromised, and likely prematurely. At that point they discover they have not been recharging them to full, then decide to treat the next set of batteries better with a charging source which willactually fully rechare them once plugged into the grid after an outing.
My battery diatribes are to help prevent batterycide. it is important to return them to a true full charge promptly, if you expect to get acceptable longevity from them.
Acceptable is however, subjective. Somebody might get 100 deep cycles from them over 3 years and think that is fine. I accumulate nearly 300 cycles a year and if a battery failed at 100 deep cycles I would be seething.
I am at year the 62 month mark on my Northstar group 27 AGM battery, with over 1000 deep cycles. I am not going to say the battery is still going strong, as I can easily see it cannot maintain the voltage it once did when starting my engine, but it is still however holding surprisingly high voltages in my regular overnight usage, powering a 12vDC 2 cubic foot fridge and a laptop and lights and fans and depleted 60 of its 90Ah capacity, can still easily start my engine in mild temperatures.
Keep the wiring between your inverter and battery short, and use thick copper. Make sure your 3 parallelled batteries take power from the + on battery one and the - of battery 3, and use tick copper with proper wire terminations on them, as thick as the inverter cables.
If you halfass the wiring you will get to do it over, at best, and worst you will burn down your van.
http://www.genuinedealz.com/custom-cables