I have 7 American Buff geese -- they do fly over my 4 ft fence, but so far I haven't had to clip wings. They can fly for short distances when excited, especially when there are strong steady winds for them to lift off on. Several of my buff geese flew easily to 7 / 8 ft at least while I was watching them, and flew probably 20 or 30 feet. I did tell them they were supposed to be too heavy to fly, but they don't listen. However, this was in a strong wind, they had a large flat open space, and it was in late winter at the start of their breeding season, so they were more excitable. It is possible it happened when the ganders were fighting and then the rest of the flock just got excited and took off. It happened several times over a month, but it has been at least a month since they have done it. They hang out next to the fence because their friends are still inside, so it wasn't hard to put them back in. If they had done it repeatedly, I would have clipped a wing, but wing clipping always makes them look so undignified, so I use it as a last resort. As far as standing next to the fence like a chicken, looking at it, and then flying over it -- I've never had them do that.
I've never had my geese crawl under my fence, but it is electrified netting. They don't touch it once they learn that it can bite back. However, if I forget to turn on the charger, they will start nibbling on it after a few days, and then they can get tangled trying to reach through to the better grass on the other side. Use rigid fencing with small holes, or wood, if you aren't going to electrify it. I
A flock of geese might intimidate some dogs. But the dog would ALMOST always win if it chose to attack. A group of geese might have success against a smaller dog, but since you can't predict what kind of dog would stray into your yard, you'd be better off using fencing.
The geese do do a great job of letting me know if anything strange is happening outside. They also have great personalities, much better than turkeys, in my option!
And don't necessarily believe that geese will not eat leaves and shoots. It depends. My geese have eaten bark off the small apple branches, leaves, and chewed up small fir trees -- all of which are not on their menu. I wouldn't trust them around anything important until you are sure they aren't going to chew on it. Some of it is just that they like to chew on random things, like a toddler, to try to figure out what they are, or just to play.