Sounds like a good plan. I've read several articles of people using geese to weed orchards and vineyards. And ducks being used to eliminate grasshoppers and other pests.
Sounds like a good plan to me. I'd start with just a few geese. They graze very short and if you put to many in there they'll have it down to a muddy trench in no time. You can always get more later if they don't keep up with it. Ideally you'll want another pasture for them so that you can...