Shelter? Heck no.
Geese don't mind the rain, don't sleep through the night, and aren't susceptible to most predators. (I don't know if you've got anything in Connecticut that we don't have in Michigan. But my geese have had no trouble with the raccoons, owls, rats, and foxes that I know are around. I
hear about cougars, but have never seen one. So I can't say they've fought any of those off. But my
chickens die despite protection, and my geese don't die despite
lacking protection. It's one of the main reasons I love them.)