I wonder about the wisdom of this - insurance companies are generally unscrupulous and greedy, and can drop a policy holder at will. I'd save calls to the insurance company for major stuff, as if the large branch went through the home's roof, and not risk pestering them for minor nuisances.
I think a call to see if the city or town has some sort of volunteer organization would be a reasonable first approach. How urban or rural is the area in question?
Art