The inverters I am familiar with don't produce a pure sine wave. But assumming that they do, the power out has to be less than the power in because nothing is 100% efficient. Since the formula for power is I x V = P (current times voltage = power), for every one amp delivered to the load at 110V you need to draw about 10 amps from the 12 volt battery. (1 amp x 110V is about equal to 10 amp x 12V) And since most systems draw a lot more than 1 amp, you would need a massive bank of 12 volt batteries to run an average system for any period of time. However, if you can afford the batteries and can get an inverter to produce a pure sine wave you may be on to something.
DC Power/AC Inverter power supply
Has anyone tried running a 12 volt DC battery with an AC inverter? There is a computer grade AC inverter that is supposed to produce a pure 117 volt AC sine wave (I don't want to mention the manufacturer). In theory this will eliminate the power grid AC grunge better than a power conditioner, even the PS audio power plants (since there are no AC artifacts ANYWHERE in the chain). I have been told that the artifacts of producing AC power in this manner far outweigh the AC grid isolation. Again, this is not an el cheapo converter. Anyone ever try this for low power draw pre-amps and digital equipment?