The electrical load it takes depends on the size of the incubator, of course, but many of the small models that hold up to 2 dozen chicken eggs don't take much power. I have a Brinsea Octagon 20 with a turner, the incubator itself is 45 watts peak load, 25 watts operating load (whatever that means, I guess it takes more for milisecond when it first turns on the heating element), and the turner takes a whopping 3 watts.
Mine can hold about 20 turkey eggs, or about 24 hens eggs, or as many as 100 Coturnix quail eggs.
This would probably be "doable" for someone off grid with the right kind of solar battery charger/backup unit. I think a lot of the small incubators in this size range are probably similar in power requirements.
