DC inverter to AC power in dash Options

[belizecelica]

Hey guys,
ive seen these power inverters in walmart and autozone to convert power to AC and they have three prong outlets like regular home outlets to power appliance and whatnot. I was thinking if this unit could be hooked up, maybe stored under the seat or somehwere out of view, and the the wires run to the outlets mounted to the dash, I was thinking that little pocket to the right of the cigarette outlet mounted nice and flush and maybe molded seamlessly with fiberglass or some plexiglass. That would be tight!! Do you think this would be possible? What wires would I run them to? the cigarette lighter wires will be too thin, so one might have to be hooked up directly to the battery with heavy gauge wire.