I'm glad to hear that you know it sounds stupid. But it's not necessarily a stupid question. It's a fascinating question. I am easily fascinated. It's more a question of ignorance than stupidity. While you can't fix stupid, you can certainly fix ignorant.
So, let's take a closer look and see why it won't work.
Charging a battery is accomplished by forcing a direct current into the cell in the reverse direction replaces energy drawn from the cell during discharge. The effect on the electrolyte and the plates during this charging process is essentially the reverse of the discharge process. Lead sulfate at the plates and the water in the electrolyte are broken down into metallic lead, lead dioxide, hydrogen and sulfate ions. This re-creation of plate materials and sulfuric acid restores the original chemical conditions including, in time, the original specific gravity.
The amount of energy it takes to re-create the original specific gravity is, of course, at least the same as the energy produced by the chemical reactions during discharge. This energy is supplied by the charger in the same form that it was removed from the battery: as volts and ampere-hours (or watt-hours and kilowatt-hours). Thus, if the battery produced 600 watt-hours (50 amp hours) during discharge, it takes at least 600 watt-hours (50 amp hours) to recharge it, plus additional watt-hours (amp hours) to make up for losses in the energy-transfer processes (heat loss and chemical energy loss).
Use of the correct charger is an important factor in maximizing the overall efficiency of the battery system. Used correctly, under proper conditions, a modern battery charger will routinely provide overall efficiencies on the order of 85% with a battery of 18-24 cells; 80% with 12 cells and 75% with a 6-cell battery. Two 6-volt batteries or a single 12-volt battery is a 6-cell battery. So, the charging efficiency will be about 75%, meaning, if you put 50 amp hours into the battery via a charger, the battery will only store 75% of that, or 37.5 amp hours. It will take 66.66 amp hours to put 50 amp hours back into the battery.
If you have a 100 amp hour battery trying to charge itself via an inverter and charger, every hour you have the charger connected you are draining the battery an additional 25% beyond what you are putting in.
But wait! There's more!
The inverter has an average electrical current transfer of energy loss of about 10%, primarily in the form of heat. So the inverter is drawing from the battery about 10% more power than it is providing. You have to add that 10% to the 25% lost in the charging process, giving you a net loss of 35% from the battery.
Now you know.
