I have (4) 12V 190 Ah AGM batteries connected in series. I want to run a portable A/C unit through a 2000 watt inverter connected to those batteries and charge the batteries simultaniously with a battery charger powered by a generator. The A/C unit requires 7.5 amps continous and 15 amps surge. I would like to do this because with the A/C unit connected to the generator, every time the compressor kicks on the generator revs up which is just annoying. My plan is to use a 100 amp charger to contiually charge the batteries while im running the A/C. I calculate that the A/C will draw approximately 83 DC amps while running.
There is no problem with having a load drawing power while a charger is charging the batteries. The charger is pushing power into the system and the A/C is taking it out again. Most of the power will be going straight from the charger to the A/C, but that just means that your battery array will take longer to charge as it'll only be getting charged at 17A as opposed to 100A (100A-83A). This is the same as when you use your laptop or phone while it's plugged in.
While this is possible, I also wanted to point out that you are converting AC to DC and then back to AC in this setup. That's a whole lot of lost power. The little "rev" you get when the compressor kicks on is a small price to pay for the extra fuel consumption! Best of luck.