Almost. The battery doesn't seem to be quite big enough to see us through the night, so we use a small amount from the grid every morning. Unless that's something to do with the inverter needing the grid connection to keep working - if the grid goes down, so does our power, so it might be the small amount is that.
It would have cost a lot more to get a system that enabled us to be completely off grid, but yes, we don't need to buy very much. A few pence every day. Overall, we are happy and hoping the bird netting thing is resolved. :)