Ellie
How long can you use the batteries before you have to charge it them back up?
It can be done you just have the scale wrong. It helps if it takes days to drain your batteries, then the solar could replace your loads as you use them. As BFL13 said though, this isn't a small project nor would you run it through the 7 pin. You would want a controller connected to the batteries. I have three big panels for 720w that can produce close to 50a aimed at the sun. In 6 hours they should at least get your batteries back up to 90%. If the sun was shining when the power went out, the 50a would cover a lot of loads saving the batteries for night time. So doable yes, small or cheap, no.