Since geese are grass eaters, if she nibbles at the hay it should be fine, since it's just dried grass

The trouble could come if she managed to eat a whole piece without chewing it into sections, since that might cause a crop impaction.
The other thing about hay is that wet hay can potentially grow aspergillosis, a fungus that can infect animals and cause respiratory disease. And of course with waterfowl, their bedding tends to get wet. Now, I don't know how much of a threat that really is, but it is something that could potentially happen.