Is this not just a change in power input but a substantially more energy efficient air conditioner, too?
I've seen small A/C systems for cars and marine applications that can run off DC power, but they're usually pretty small which helps cut the overall power consumption. In marine applications they also have the advantage of being able to use sea water to move the heat versus a fan and coils in open air.
One of Sharp's smallest split system units has 8500 BTU of cooling with an EER of 13 which is roughly 650 watts. That's about 14 amps @ 48v, 27 @ 24, and a battery sucking 54 amps at 12v (run with welding cable).
8500 BTU might cool a room reasonably well, but its not going to provide whole-house cooling, either, and would require a pretty large battery array to run off battery. It might make sense for some kind of supplemental cooling setup where it ran direct off solar panels.