I would think that you could cut off the other circuits, and be able to run the A/C. And hopefully, the outlet is a dedicated circuit, without other things drawing off it.
You may want to buy one of those "Kill a Watt" watt meters, and check to see what the load is actually being drawn by your system.
After all, your lights and such will be on the batteries.....and you can charge them with the converter when the A/C is off during the day.
Of course, if you do run just the A/C, you don't want to run any other 110VAC item (such as microwave).