My impression is that the geese aren't too fussed about birds. Cats and dogs, yes. But it's hard to tell because whenever I'm around, the crows aren't, iykwim. Certainly I've had no egg stealing but the hens are in a henhouse so they'd have to go in through the pop hole, across the house and into the nest boxes (and a longshot to actually find an egg there anyway). Could you do what you do with egg eating hens and put lots of false eggs in there - would they give up if they kept getting a golf ball instead? You can also get those nest box things that have the eggs roll away into a covered area which is also intended to prevent hens eating eggs but might also work for crows?
H