You could certainly run anything off of batteries, the real question is: can you afford that many batteries? are you comfortable with the inherent innefficiency in such a system? I dont think the electric company looks at spikes, I thought they just looked at total KWH at the end of the month, but i dont know.
That said, It could be done. The simplest way would probably be car batteries in parallel and a 1kwatt car inverter, that aught to be able to run a couble 400watt lamps.
Car batteries are rated in watthours. the biggest ive seen are arround 80 watthours. so for 400 watthours, you'd need 5. That would run 400 watts for an hour or 1 watt for 400 hours. to run 400 watts for 12 hours you'd need 60. (This is not factoring in the inneficiency of the inverter or the inneffeciency of the batteries, the actual figure might be like 65 or something) 60 car batteries would be over $3000. Car batteries, deep cycled like this, would have a very poor lifespan. I wouldnt expect any of them to last more than 5 years. This might be something to consider on a HUGE grow, but realize, those 60 batteries are only going to power _one_ 400 watt bulb for 12 hours. Probably more costly than its worth.
An easier, cheaper and far more effecient way of removing the spikes though, would be to have two flower rooms, each on 12/12, but on opposite light cycles, so that you have a constant electrical draw....