Yes you can show geese. the American Poultry Association is like the American Kennel Club is for dogs. They publish the Standards and train and regulate the judges. The shows cover waterfowl (geese and ducks) Large and bantam Chickens, Turkeys, and guinnae fowl. Geese are part of Waterfowl. and there are 3 classes, heavy, medium, and light. Pilgrims are in the medium class but very seldom win even their class due to stiff compention from other medium geese. If they win their class they compete for best and reserve goose. which compete against all the ducks to determine best and reserve waterfowl which then compete against the other classes to determine the best of show.
BTW poking or messing with the birds at these shows is likely to get you ejected from the show hall!
International Waterfowl Breeders Association is likely to be more exotic, "wild" waterfowl rather than the old standard type birds.
If you have any real interest in showing your birds, Join the APA and subscribe to the Poultry Press for all the info on shows, Shows are most often held in the fall of the year so not to interfer with the breeding cycles