Yes, that is exactly what is happening. 2000W solar panels feed the battery, up to 800W are allowed to be fed back into the grid/house network. Keep in mind you could also plug a 3000W device directly into the battery, meaning you could power a lot more than that if it is not connected to the grid. If you have devices that need little power for a long duration or high power for a short duration they can be fed with 100% solar that way. Depending on your use case that can save further money.
