The inverter costs in efficiency, i.e. converts some of those watt-hours to heat instead of 120 electric, but the battery watt-hours is still the same. The efficiency of an inverter depends on the size and loading, as well as the design quality of the device, but 90% is a fair rule of thumb estimate.
Two 6V batteries in series will have double the watt-hours (same amperage at 2x the voltage = 2x the wattage).
You should also be aware that the battery watt-hours is not a fixed number. The amount of usable power (watt-hours) varies with the amp load on the battery. The lower the amp load, the greater the number of watt-hours available (Peukert's Law). Furthermore, the storage capacity deteriorates with age and use, so the spec amp hours generally apply only to a new battery in laboratory conditions.
Last, an inverter usually shuts off at 10.5v and may give an warning alarm at 11.0v The 10.5v figure is the same as the low cut-off used to calculate the 20 hR discharge rate and the 1350 watt (per 6v battery) capacity, so in theory the inverter can use all 1350 watts. However, conventional wisdom is that discharging a battery all the way to shut-down will damage it and severely reduce its longevity, so a max discharge of 50% (roughly 12.0v) is recommended. That reduces the available watt-hours substantially.