The answer, apparently, is “not usually.”
Geese, famous for their copious defecation, are less likely to defecate when they are flying than when they are grazing and walking on the ground, and they tend to empty their cloacas upon takeoff, cutting down on the risk to bystanders, said Laura Erickson, science editor at the Cornell Laboratory of Ornithology. Also, she said, geese tend to take off in a direction away from people, and the droppings quickly break up into small packets in the air.
Oh man. My friends in the Society for the Study of Goose Defecation are gonna be sooooo into this.
Aerial Peril [NY Times]