Technicaly it is connected through the breaker so you could only supply as much to the rest of the house as that breaker can pass. Not ideal or the proper way of doing it though. Also the reason to disconnect from the grid is that you could start feeding downed power lines, and if line workers go out to work on the lines they can be electrocuted. Also, theres no telling when power will return. There should be a separete input for the generator and a transfer switch to switch between the generator and grid.
There’s a reason why home battery storage systems needs to be connected to the breaker panel. You route power through it. When the batteries aren’t needed then it’s just a dumb relay for grid power. When you’re drawing power from batteries it disconnects the grid.
Only a few industries ever draw power both from grid and local power sources at once (during peak load) and they route all the power sources through a power distribution system which prevents backfeeding.
