Grid tied inverters and a gas generator?

Hey everyone, I have a 2 kw solar installation in my home using arround 8 emphase grid tied inverters. Power doesn’t usually go out in my zone but sometimes it does go out, and I have a friend that lends me their generator when this happens.

If I leave the solar installation plugged into my circuit, will it continue generating therefore reducing the load in the generator? Where will the excess that I usually just sell to the grid go? Can it blow the generator or something? Same question for a Bluetti battery that sometimes I get to power my whole home.

I know the obvious Awenser is to just try it, but replacing the whole system isn’t so obvious if something happens 😂

Any help to solve my questions will be appreciated