Yes, they are very efficient as heaters and air conditioners. I am working on installing one (12,000 BTU) that will heat and cool 700 sq ft; using 900 Watts total.
LiIon batteries can be deep cycled 15,000 times with no reduction in capacity. They will work long past that, at a slightly reduced capacity.
Figure 10 watts, at 4 volts per cell. From that you can combine anything you need! :)