The first big problem I see here, in case you missed it, is that to run a 480V motor your VFD DC bus will have to be somewhere around 650VDC; not easy with batteries because they need to be an a long series string to get there. That's why Mike's example looks so extreme. So let's say you used 12VDC automotive batteries instead. That still means 650/12 = 55 batteries in series just to get to the voltage level you need. Then you have to look at the possibility of voltage drop under use, so you have to over shoot a bit, then deal with possible over voltage effects.
Doing this with batteries alone is not likely a great solution, you might be better off using something designed to do this already, such as a UPS system. The difference is, they will have a DC boost converter inside that can deal with getting to the necessary DC bus level without having to add so many batteries in series, so then all you need to worry about is the amp-hours necessary to survive your 14 seconds, which will be much more reasonable. You could, if you are so inclined, construct your own DC boost converter from scratch I suppose, but I'm of a mind to not try to re-invent something that someone else already mass produces. It never works out well for me. The UPS will have the DC boost converter, the trickle charger and the batteries already. Done.
"Will work for (the memory of) salami"